Solving a Quadratic by Completing the Square

1
Solving a Quadratic by Completing the Square
8-Jan-10
Solve by completing the square x2 6x 8 0
B ? A Topic
2
Try to factorise and solve x2 6x 8 0 (x
)(x ) 0
Find the factor pairs of -8. 1 x -8 2 x
-4 4 x -2 8 x -1 From these choose the
two that add up 6 Help!
3
Complete the square x2 6x 8 0 (x )2
8 0 (x 3)2 8 32 0 (x 3)2 8 9
0 (x 3)2 17 0 (x 3)2 17 (x 3)
v17 x v17 3 and -v17 - 3 x 1.12 and
7.12
Half of the x terms number 6 ? 3
Get rid of the square with a v
Half of the x terms number squared 6 ? 32
Numbers have a positive and negative square root
4
Complete the square x2 - 8x 5 0 (x - )2
5 0 (x - 4)2 5 42 0 (x - 4)2 5 16
0 (x - 4)2 11 0 (x - 4)2 11 x - 4 v11 x
- 4 v11 4 and -v11 4 x 7.32 and 0.69

Half of the x terms number 8 ? 4
Get rid of the square with a v
Half of the x terms number squared 8 ? 42
Numbers have a positive and negative square root
5

• Try
• x2 6x 2 0
• x2 4x 4 0
• x2 - 8x 2 0

X2 6x - 2 0 (x - _ )2 2 _ 0 (x _ )
2 - _ 0 (x _ )2 _ 0 (x - _ )2 __ x -
_ v11 x and x and
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(x 3)2 means (x 3)(x 3) x2 3x 3x 9 x2
6x 9
What is (x 3)2?
B x2 6x 9
A 2x 6
B x2 6x 9
Do not make this classic mistake
C x2 6x
D x2 9
11
(No Transcript)
12
Middle number is doubled
This way its a half
13
1. Solve by completing the square x2 8x - 12
0
x2 8x 12 0 (x 4)2 12 42 0 (x
4)2 28 0 (x 4)2 28 x 4 v28 x 4
v(4 x 7) x -2v7 4 and 2v7 - 4 x -8.5826 and
0.5826
14
2. Solve by completing the square 4x2 32x 44
0 Give your answer to 4 d.p.
Divide all the terms by the value of the x2
coefficient (i.e. 4) so as to obtain x2
4x2 32x - 44 0 x2 8x 11 0 (x 4)2
11 42 0 (x 4)2 27 x 4 v27 x 4 v(3
x 9) x 4 3v3