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: 25


The solutions are $-6+3\sqrt{2}$ and $-6-3\sqrt{2}$.

Work Step by Step

$ x^{2}+12x+18=0\qquad$ ... write left side in the form $x^{2}+bx$ (add $-18$ to each side). $ x^{2}+12x+18-18=-18\qquad$ ...simplify. $ x^{2}+12x=-18\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{12}{2})^{2}=6^{2}=36\qquad$ ...add $36$ to each side of the expression $ x^{2}+12x+36=-18+36\qquad$ ...simplify. $ x^{2}+12x+36=18\qquad$ ... write left side as a binomial squared. $(x+6)^{2}=18\qquad$ ...take square roots of each side. $ x+6=\pm\sqrt{18}\qquad$ ...rewrite $\sqrt{18}$ as $\sqrt{9\cdot 2}$ $ x+6=\pm\sqrt{9\cdot 2}\qquad$ ...evaluate $\sqrt{9}$. $ x+6=\pm 3\sqrt{2}\qquad$ ...add $-6$ to each side. $ x+6-6=\pm 3\sqrt{2}-6\qquad$ ...simplify. $x=-6\pm 3\sqrt{2}$
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