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?

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

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

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

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.

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.

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.

Example 1 Continued Step 5: Solve for x.

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.

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.

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.

Example 2 Continued Step 5: Solve for x.

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

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

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