Solve.

Question of the Day

CCGPS Geometry Day 62 ( ) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: When is it useful to solve quadratics by completing the square? Standard: MCC9-12..A.REI.4b

Completing the Square Completing the square is used for all those not factorable problems!! It is used to solve these equations for the variable. It gets a little messy when a is not 1.

Perfect Square Trinomials Examples l x 2 + 6x + 9 l x x + 25 l x x + 36

Creating a Perfect Square Trinomial l In the following perfect square trinomial, the constant term is missing. x x + ____ l Find the constant term by squaring half the coefficient of the linear term. l (14/2) 2 x x + 49

Perfect Square Trinomials Create perfect square trinomials. l x x + ___ l x 2 - 4x + ___ l x 2 + 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

x 2 + 4x – 4 = 0x 2 – 2x – 1 = 0

Example 4 Finding Complex Solutions x 2 - 8x + 36 = 0x 2 +6x = - 34

Example 5 Solving When a≠0