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 - Guided Practice for Examples 3, 4, and 5 - Page 286: 11


The solutions are $-4+3\sqrt{2}$ and $-4-3\sqrt{2}$.

Work Step by Step

$ 6x(x+8)=12\qquad$ ... use the Distributive Property. $ 6x^{2}+48x=12\qquad$ ...divide each term with $6$. $ x^{2}+8x=2\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{8}{2})^{2}=4^{2}=16\qquad$ ...add $16$ to each side of the expression $ x^{2}+8x+16=2+16\qquad$ ... write left side as a binomial squared. $(x+4)^{2}=2+16\qquad$ ...simplify. $(x+4)^{2}=18\qquad$ ...take square roots of each side. $ x+4=\pm\sqrt{18}\qquad$ ...add $-4$ to each side of the expression $ x+4-4=\pm\sqrt{18}-4\qquad$ ...simplify. $ x=-4\pm\sqrt{18}\qquad$ ...rewrite $\sqrt{18}$ as $\sqrt{9\cdot 2.}$ $ x=-4\pm\sqrt{9\cdot 2}\qquad$ ...evaluate $\sqrt{9}$. $x=-4\pm 3\sqrt{2}$
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