Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Skill Practice - Page 288: 34


Answer: A

Work Step by Step

$ x^{2}+10x+8=-5\qquad$ ... write left side in the form $x^{2}+bx$ (add $-8$ to each side). $ x^{2}+10x+8-8=-5-8\qquad$ ...simplify. $ x^{2}+10x=-13\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{10}{2})^{2}=(5)^{2}=25\qquad$ ...add $5$ to each side of the expression $ x^{2}+10x+25=-13+25\qquad$ ...simplify. $ x^{2}+10x+25=12\qquad$ ... write left side as a binomial squared. $(x+5)^{2}=12\qquad$ ...take square roots of each side. $ x+5=\pm\sqrt{12}\qquad$ ...rewrite $\sqrt{12}$ as $\sqrt{4\cdot 3}$ $ x+5=\pm\sqrt{4\cdot 3.}\qquad$ ...evaluate $\sqrt{4}$. $ x+5=\pm 2\sqrt{3}\qquad$ ...add $-5$ to each side. $ x+5-5=\pm 2\sqrt{3}-5\qquad$ ...simplify. $x=-5\pm 2\sqrt{3}$
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