1. Completing the Square

2. Factor these quadratic equations:
x2 + x – 12
x2 – 13x + 30
x2 + 6x + 9

3. Now, multiply these factors:
(x + 4)(x + 4)
(x – 6)(x – 6)
notice the pattern??

4. “Completing the Square”
x2 + 6x + _____
= (x )2
STEP ONE: Take the “x” coefficient and divide by 2.
STEP TWO: Square the result from step one and put as the final term of the quadratic.
STEP THREE: Factor the quadratic. It’s a perfect square!

5. “Complete” these squares:
x2 – 14x + ______
= (x )2
x2 + 10x + ______
x2 + x + _______

6. How is this useful?
When we can’t factor out a quadratic, such as this:
x2 + 6x + 4 = 0

7. How is this useful? Or this one: 2x2 – 8x – 2 = 0
**x2 term must have a coefficient of 1 in order to be able to “complete the square”**

8. HOMEWORK:
p.512 #73-84