Solving Quadratic Equations By Completing the Square Find

Solving Quadratic Equations By Completing the Square

Find Perfect Square Quadratics Examples: x 2 + 6 x + 9 = (x+3)2 x 2 – 10 x + 25 = (x – 5)2 x 2 + 12 x + 36 = (x + 6)2

Engineer/Create a Perfect Square Quadratic The constant term is missing from this perfect square quadratic. ax 2 + bx + c For a perfect square c = (b/2) 2 x 2 + 14 x + ____ Find the constant term by squaring half the coefficient of the linear term. c = (b/2) 2 (14/2) 2 x 2 + 14 x + 49

Engineer/Create Perfect Square Quadratics x 2 + 20 x + _100_ Example: (20/2)2 = 100 x 2 – 4 x + _____ x 2 + 5 x + _____

“Complete the Square” to solve the Quadratic Equation Solve the following equation by completing the square: x 2 + 8 x – 20 = 0 Step 1: Isolate the terms with variables on one side. x 2 + 8 x = 20

STEP 2: Solve by Completing the Square Step 2: Find the term that completes the square on the quadratic side of the equation. Add that term to both sides. x 2 + 8 x + ____ = 20 + ____ Note (8/2)2 = 42 = 16 x 2 + 8 x + 16 = 20 + 16

STEP 3: Solve by Completing the Square Step 3: Factor the quadratic side of the equation and simplify the constant side. x 2 + 8 x + 16 = 20 + 16 x 2 + 8 x + 16 = 36 (x + 4) ( x + 4) = 36 (x + 4) 2 = 36

STEP 4: Solve by Completing the Square •