Equations Quadratic in Form

1
Equations Quadratic in Form
Sec 10.3
2
Equations Quadratic in Form
Sec 10.3
ex Solve a.
3
Equations Quadratic in Form
Sec 10.3
ex Solve a.
4
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
5
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
6
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
7
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
8
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
9
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
10
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
11
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
12
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
13
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
or
14
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
or
or
15
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
or
or
or
16
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
or
or
or
or
or
x 2
17
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
or
or
or
or
or
x 2 or x
18
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
or
or
or
or
or
x 2 or x
19
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
NOTE
or
or
or
or
or
x 2 or x
20
Equations Quadratic in Form
Sec 10.3
ex Solve a.
x2
x2
x2
x2
4x2 7x 2 0
a 4 b 7 c 2
NOTE
(4x 1)(x 2) 0
or
or
or
or
or
x 2 or x
21
Equations Quadratic in Form
Sec 10.3
ex Solve b.
22
Equations Quadratic in Form
Sec 10.3
ex Solve b.
23
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
24
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
25
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
26
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
27
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
28
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
29
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 20x
30
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 72 20x 72
31
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 72 20x 72
32
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 72 20x 72
0 11x2 79x 72
33
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 72 20x 72
0 11x2 79x 72
0 (11x 9)(x 8)
34
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 72 20x 72
0 11x2 79x 72
0 (11x 9)(x 8)
(11x 9) 0 or (x 8) 0
35
Equations Quadratic in Form
Sec 10.3
ex Solve b.
4x(x 9)
4x(x 9)
4x(x 9)
8(x 9) 12x 11x(x 9)
8x 72 12x 11x2 99x
20x 72 11x2 99x
20x 72 20x 72
0 11x2 79x 72
0 (11x 9)(x 8)
(11x 9) 0 or (x 8) 0
x or x 8
36
Equations Quadratic in Form
Sec 10.3
ex Solve c.
37
Equations Quadratic in Form
Sec 10.3
ex Solve c.
38
Equations Quadratic in Form
Sec 10.3
ex Solve c.
39
Equations Quadratic in Form
Sec 10.3
ex Solve c.
40
Equations Quadratic in Form
Sec 10.3
ex Solve c.
41
Equations Quadratic in Form
Sec 10.3
ex Solve c.
(4x 3)(4x 1) 0
42
Equations Quadratic in Form
Sec 10.3
ex Solve c.
(4x 3)(4x 1) 0
43
Equations Quadratic in Form
Sec 10.3
ex Solve c.
(4x 3)(4x 1) 0
44
Equations Quadratic in Form
Sec 10.3
ex Solve d.
45
Equations Quadratic in Form
Sec 10.3
ex Solve d.
( ) ( ) 0
46
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 ) (x2 ) 0
47
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
48
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4)
0
49
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4) (x 1)(x 1) 0
50
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4) (x 1)(x 1) 0
51
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4) (x 1)(x 1) 0
52
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4) (x 1)(x 1) 0
53
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4) (x 1)(x 1) 0
54
Equations Quadratic in Form
Sec 10.3
ex Solve d.
(9x2 16) (x2 1) 0
(3x 4)(3x 4) (x 1)(x 1) 0
55
Equations Quadratic in Form
Sec 10.3
ex Solve e.
56
Equations Quadratic in Form
Sec 10.3
ex Solve e.
57
Equations Quadratic in Form
Sec 10.3
ex Solve e.
58
Equations Quadratic in Form
Sec 10.3
ex Solve e.
59
Equations Quadratic in Form
Sec 10.3
ex Solve e.
60
Equations Quadratic in Form
Sec 10.3
ex Solve e.
61
Equations Quadratic in Form
Sec 10.3
ex Solve e.
62
Equations Quadratic in Form
Sec 10.3
ex Solve e.
63
Equations Quadratic in Form
Sec 10.3
ex Solve e.
64
Equations Quadratic in Form
Sec 10.3
ex Solve e.
x 27 or x 1
65
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
66
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
67
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
68
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
69
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
70
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
71
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
72
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
73
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
74
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
75
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
76
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
22950 90r
So
77
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
22950 90r
So
90 90
78
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
22950 90r
So
90 90
255mph r
79
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
22950 90r
So
90 90
255mph r
80
Equations Quadratic in Form
Sec 10.3
ex Solve f.
NOTE
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
22950 90r
So
90 90
255mph r
81
Equations Quadratic in Form
Sec 10.3
ex Solve f.
NOTE
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind in
the same time that he traveled 720 miles against
the wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind
So
82
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
83
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
84
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
85
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
86
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
87
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
88
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
89
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
So
90
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
0 6r2 1530r
So
91
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
0 6r2 1530r
So
0 6r(r 255)
92
Equations Quadratic in Form
Sec 10.3
ex Solve f.
Watson flew his plane for 6 hours at a constant
speed. He traveled 810 miles with the wind, then
turned around and traveled 720 miles against the
wind. The wind speed was a constant 15 mph.
Find the speed of the plane.
Let r the rate (speed) of the plane
NOTE d rt
twith wind tagainst wind 6
0 6r2 1530r
So
0 6r(r 255)
255mph r
93
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
94
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone
95
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
96
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


97
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


98
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together



99
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together




100
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


5t(t2)
5t(t2)
5t(t2)


101
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


5t(t2)
5t(t2)
5t(t2)


102
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


5t(t2)
5t(t2)
5t(t2)


5t 5(t 2) t (t
2)
103
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


5t(t2)
5t(t2)
5t(t2)


5t 5(t 2) t (t
2)
5t 5t 10 t2
2t
104
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


5t(t2)
5t(t2)
5t(t2)


5t 5(t 2) t (t
2)
5t 5t 10 t2
2t
10t 10 t2 2t
105
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
5t(t2)
5t(t2)


5t 5(t 2) t (t
2)
5t 5t 10 t2
2t
10t 10 t2 2t
106
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


5t 5(t 2) t (t
2)
5t 5t 10 t2
2t
10t 10 t2 2t
107
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
5t 5t 10 t2
2t
10t 10 t2 2t
108
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
t 4
5t 5t 10 t2
2t
10t 10 t2 2t
109
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
t 4
5t 5t 10 t2
2t
t 4
10t 10 t2 2t
110
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
t 4
5t 5t 10 t2
2t
t 4
10t 10 t2 2t
111
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
t 4
5t 5t 10 t2
2t
t 4
10t 10 t2 2t
112
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
t 4
5t 5t 10 t2
2t
t 4
10t 10 t2 2t
t 2
113
Equations Quadratic in Form
Sec 10.3
ex Solve g.
A temporary job agency provides two people to
clean an office building. Working together, the
two can clean the building in 5 hours. One
person is new to the job and takes 2 hours longer
than the other person to clean the building
alone. How long (to the nearest tenth) would it
take the new worker to clean the building alone?
Let t the amount of time it would takes for
the experienced worker to clean

the building alone Let
t 2 the amount of time it would takes for
the new worker to clean the

building alone
rate of the new worker
rate of the experienced worker
rate of the workers working together


10 t2 8t
5t(t2)
10 16 t2 8t 16
5t(t2)
5t(t2)


26 (t 4)2
5t 5(t 2) t (t
2)
t 4
5t 5t 10 t2
2t
t 4
10t 10 t2 2t
t 2