Solve for x:

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Warm-up

• Solve for x
• 2. 5x-18 7x
• Simplify(no decimals)
• 3. v32 4. v36 5. v14 6. 2v20

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Solving Quadratic Equations
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x the x-intercepts
a.k.a. roots or solutions

• There are several methods to solve for x
• Factor
• Solve by Square Root
• Graphing

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Quadratic Equation
Before you can solve, the equation must be in
Standard Form
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1) 5x2 8x 0
Factor
Set each factor equal to 0 and solve for x.
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2) 2x2 7x 0
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3)
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You try
4)
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x2 4x 2 -1
5)
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x2 - 4x -3x 3
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set 0
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Warm-up

• Solve by factoring.
• Graph the equation in the calculator. What do you
  observe?

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Solving Quadratic Equations by finding Square
Roots
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Square Root
What is a square root?
The number that it takes to make a perfect square
When you have a pair, bring the number out.
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We will get x squared by itself.
Then we will take the square root of both sides
of the equal sign.
There will be a positive answer and a negative
answer.
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A Refresher on Inverses (opposites)

• Opposite of Multiply is ____________
• Opposite of Add is ____________
• Opposite of Divide is ____________
• Opposite of Subtract is ____________
• Opposite of squaring is ____________
• Opposite of square rooting is ____________

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Lets look at some examples where x2 is already
by itself.
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Examples. Solve the equation. Write the
solutions as integers if possible. Otherwise,
write them as radical expressions.
Here, all we have to do is take the square root
of both sides.
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Lets look at some examples where x2 is NOT by
itself.
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We must solve to get x2 by itself 1st!
add 48
divide by 3
take the square root of both sides
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We must solve to get x2 by itself 1st!
subtract 32
take the square root of both sides
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You try!
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Think about these numbers.
Plug this in your calculator. What do you get?????
Therefore, there is NO REAL SOLUTION b/c the
square of a number is NEVER negative
The only solution is zero b/c zero is not
positive or negative
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Practice