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Quadratic Equations: Completing the Square Example & Practice

Learn how to solve quadratic equations using the completing the square method through step-by-step examples and standardized test practice questions. Check your solutions to ensure accuracy.

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Quadratic Equations: Completing the Square Example & Practice

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  1. Add , or (–8)2, to each side. –16 2 2 EXAMPLE 2 Solve a quadratic equation Solve x2 – 16x = –15 by completing the square. SOLUTION x2 – 16x = –15 Write original equation. x2 – 16x + (– 8)2=–15 + (– 8)2 (x – 8)2 = –15 + (– 8)2 Write left side as the square of a binomial. (x – 8)2 = 49 Simplify the right side.

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

  3. (15)2– 16(15) –15 (1)2– 16(1) –15 –15 = –15 –15 = –15 ? = ? = EXAMPLE 2 Standardized Test Practice CHECK You can check the solutions in the original equation. If x = 1: If x = 15:

  4. 10 2 , or52, to each side. Add 2 EXAMPLE 3 Solve a quadratic equation in standard form Solve 2x2 + 20x – 8 = 0 by completing the square. SOLUTION 2x2 + 20x – 8 = 0 Write original equation. 2x2 + 20x = 8 Add 8 to each side. x2 + 10x = 4 Divide each side by 2. x2+ 10x + 52= 4 + 52 (x + 5)2 = 29 Write left side as the square of a binomial.

  5. ± x + 5 = 29 ± 29 x = –5 ANSWER The solutions are – 5 + 29 0.39 and – 5 – 29 –10.39. EXAMPLE 3 Solve a quadratic equation in standard form Take square roots of each side. Subtract 5 from each side.

  6. ANSWER 1, 3 ANSWER ANSWER 9.12, 0.88 1.35, 6.65 for Examples 2 and 3 GUIDED PRACTICE 4. x2 – 2x = 3 5. m2 + 10m = –8 6.3g2 – 24g+ 27 = 0

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