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 289: 54


The solutions are $-1-4\sqrt{2}$ and $-1+4\sqrt{2}$.

Work Step by Step

$ 7q^{2}+10q=2q^{2}+155\qquad$ ...add $-2q^{2}$ to each side $ 5q^{2}+10q=155\qquad$ ...divide the entire expression with $5$. $ q^{2}+2q=31\qquad$ ...square half the coefficient of $q$. $(\displaystyle \frac{2}{2})^{2}=1^{2}=1\qquad$ ...complete the square by adding$ 1$ to each side of the expression $ q^{2}+2q+1=31+1\qquad$ ...Write $q^{2}+2q+1$ as a binomial squared. $(q+1)^{2}=32\qquad$ ...take square roots of each side. $ q+1=\pm\sqrt{32}\qquad$ ...simplify $\sqrt{32}=\sqrt{4\cdot 4\cdot 2}=4\sqrt{2}$ $ q+1=\pm 4\sqrt{2}\qquad$ ...add $-1$ to each side. $q=-1\pm 4\sqrt{2}$
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