1. Warm-Up Set 1: Factor. 1) x2 + 6x + 9 2) x2 - 10x + 25 Set 2: Factor.
Question: What is the difference between the factored forms in Set One as compared to Set Two?

2. Perfect Square Trinomials
Examples:
x2 + 6x + 9
x2 - 10x + 25
x2 + 12x + 36

3. Creating a Perfect Square Trinomial
In the following perfect square trinomial, the constant term is missing: x2 + 14x + ____
To find the constant term:
______________________________.
So… x2 + 14x + ____
divide “b” by 2 then square your answer 49

4. Perfect Square Trinomials
Directions: Create perfect square trinomials.
x2 + 20x + ___
x2 - 4x + ___
x2 + 5x + ___

5. Example 1 Solving by Completing the Square
Solve the following equation by completing the square:
Step 1: Rewrite so all terms containing x are on one side.

6. Example 1 Continued
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

7. Example 1 Continued
Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
Step 4: Take the square
root of each side.

8. Example 1 Continued
Step 5: Solve for x.

9. Example 2 Solving by Completing the Square
Solve the following equation by completing the square:
Step 1: Rewrite so all terms containing x are on one side.

10. Example 2 Continued
Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

11. Example 2 Continued
Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.
Step 4: Take the square
root of each side.

12. Example 2 Continued
Step 5: Solve for x.

13. Solve each by Completing the Square
x2 + 4x – 4 = 0
x2 – 2x – 1 = 0

14. Example 4 Finding Complex Solutions
x2 - 8x + 36 = 0
x2 +6x = - 34

15. Example 5 Solving When a≠0
5x2 = 6x + 8
2x2 + x = 6