1. Solving Quadratics By Completing the Square

2. Review
Solve for x
When you take the square root, You MUST consider the Positive and Negative answers.

3. Solve for x
But what happens if you DON’T have a perfect square on one side…….
You make it a Perfect Square
Use the relations on next slide…

4. To expand a perfect square binomial:
Short Cut
To expand a perfect square binomial:
We can use these relations to find the missing term….To make it a perfect square trinomial that can be factored into a perfect square binomial.
Then

5. Make this a perfect square trinomial
Take ½ middle term
Then square it
The resulting trinomial is called a perfect square trinomial,
which can be factored into a perfect square binomial.

6. Solve by completing the square
Make one side a perfect square
Add a blank to both sides
Divide “b” by 2
4. Square that answer.
Add it to both sides
Factor 1st side
Square root both sides
Solve for x
Solve by completing the square 1.

7. Solve by completing the square
Move constant to other side.
Add a blank to both sides
Divide “b” by 2
4. Square that answer.
Add it to both sides
Factor 1st side
Square root both sides
Solve for x
Solve by completing the square 2.

8. Solve by completing the square
Move constant to other side.
Add a blank to both sides
Divide “b” by 2
Square that answer.
Add it to both sides
Factor 1st side
Square root both sides
Solve for x
Solve by completing the square 3.

9. Solve by completing the square
Move constant to other side.
Add a blank to both sides
Divide “b” by 2
Square that answer.
Add it to both sides
Factor 1st side
Square root both sides
Solve for x
Solve by completing the square 4.

10. Steps to solve Quadratics by completing the square:
Move the constant to side by itself.
Make the side (w/variables) a perfect square by adding a certain number to both sides.
To calculate this number
Divide “b” (middle term) by 2
Then square that answer
Take the square root of both sides of eq
Then solve for x

11. In a perfect square, there is a relationship between the coefficient of the middle term and the constant term.