1. Warm Ups
Solve the following quadratic equations: 1) 2x2 – 12x = 0 2) r2 + 8r + 16 = 0 3) 5x2 - 40x + 75 = 0 4) n2 – 8 = -7n

2. 3.3 Notes: Completing the Square

3. What does it mean to complete a square?
We want our last number (c value) to be a perfect square.
X2 – 10x + _______ has a perfect square at the end that has factors adding to -10.

4. Let’s try these: X2 + 8x + ______ X2 + 14x + ______ X2 – 12x + _______
What are we doing to find these numbers, in general?

5. What if the “b” value is odd?
That’s okay….we will just have a fraction  We are NOT scared of fractions!
X2 – 3x + _____
X2 + 9x + _____
X2 + x + ______

6. p. 116 #

7. So…..let’s solve now. Rules:
1) there cannot be a coefficient except 1 for “a”
2) You must move the “c” value to the right of the equal sign
3) Whatever you add to one side you MUST add to the other!

8. Example:
X2 – 6x + 4 = 0
X2 + 4x + 1 = 0

9. X2 + 4x = 12
X2 + 5x + 2 = 0

10. p. 116 #

11. Warm Up: Solve the following quadratic equations using C.T.S.
1) x2 + 2x = 9
2) u2 – 4u = 2u + 35
3) 2x2 – 12x = 14

12. What if the “a” value is NOT 1?
Well, we have one extra step then. Divide EVERYTHING!!!! By the “a” value!
Then, use the steps we did on the last notes for C.T.S.

13. Let’s try this!
2x2 + 3x – 4 = 0

14. 2x2 – 4x – 1 = 0

15. 4x2 – 4x + 3 = 0

16. Solve by C.T.S.