EXAMPLE 2 Solve a quadratic equation Solve x

EXAMPLE 2 Solve a quadratic equation Solve x 2 – 16 x = – 15 by completing the square. SOLUTION x 2 – 16 x = – 15 x 2 – 16 x + (– 8)2 = – 15 + (– 8)2 Write original equation. Add – 16 2 2 , or (– 8)2, to each side. (x – 8)2 = – 15 + (– 8)2 Write left side as the square of a binomial. (x – 8)2 = 49 Simplify the right side.

EXAMPLE 2 Standardized Test Practice x – 8 = ± 7 x=8± 7 Take square roots of each side. Add 8 to each side. ANSWER The solutions of the equation are 8 + 7 = 15 and 8 – 7 = 1.

EXAMPLE 2 Standardized Test Practice CHECK You can check the solutions in the original equation. If x = 15: ? – 15 (15)2 – 16(15) = – 15 If x = 1: ? – 15 (1)2 – 16(1)= – 15

EXAMPLE 3 Solve a quadratic equation in standard form Solve 2 x 2 + 20 x – 8 = 0 by completing the square. SOLUTION 2 x 2 + 20 x – 8 = 0 Write original equation. 2 x 2 + 20 x = 8 Add 8 to each side. x 2 + 10 x = 4 x 2 + 10 x + 52 =4+ (x + 5)2 = 29 Divide each side by 2. 52 Add 10 2 2 , or 52, to each side. Write left side as the square of a binomial.

EXAMPLE 3 Solve a quadratic equation in standard form x + 5 = ± 29 x = – 5 ± 29 Take square roots of each side. Subtract 5 from each side. ANSWER The solutions are – 5 + 29 0. 39 and – 5 – 29 – 10. 39.

GUIDED PRACTICE for Examples 2 and 3 4. x 2 – 2 x = 3 ANSWER 1, 3 5. m 2 + 10 m = – 8 ANSWER 6. 9. 12, 0. 88 3 g 2 – 24 g + 27 = 0 ANSWER 1. 35, 6. 65