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 - Quiz for Lessons 4.5-4.7 - Page 291: 3


$m=-5\displaystyle \pm\frac{\sqrt{2}}{2}$

Work Step by Step

$ 16(m+5)^{2}=8\qquad$ ...divide the entire expression with $16$. $(m+5)^{2}=\displaystyle \frac{1}{2}\qquad$ ...take square roots of each side. $ m+5=\pm\sqrt{\frac{1}{2}}\qquad$ ...add $-5$ to each side. $ m=-5\displaystyle \pm\frac{1}{\sqrt{2}}\qquad$ ...rationalize the radical by multiplying both the numerator and denominator with $\sqrt{2}$. $\displaystyle \frac{1}{\sqrt{2}}=\frac{1\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\frac{\sqrt{2}}{2}$ $m=-5\displaystyle \pm\frac{\sqrt{2}}{2}$
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