Algebra 2 (1st Edition)

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

Chapter 4 Quadratic Functions and Factoring - 4.5 Solve Quadratic Equations by Finding Square Roots - 4.5 Exercises - Skill Practice - Page 270: 32


The solutions are $2$ and $6$

Work Step by Step

$ 7(x-4)^{2}-18=10\qquad$ ...add $18$ to each side. $ 7(x-4)^{2}-18+18=10+18\qquad$ ...simplify. $ 7(x-4)^{2}=28\qquad$ ...divide each side with $7$. $(x-4)^{2}=4\qquad$ ...take square roots of each side. $\sqrt{(x-4)^{2}}=\sqrt{4}\qquad$ ...simplify. ...When solving an equation of the form $x^{2}=s$ where $s>0$, we find both the positive and negative solutions. $(x-4)=\pm\sqrt{4}\qquad$ ...evaluate $\sqrt{4} $ ($\sqrt{4}=2$) $ x-4=\pm 2\qquad$ ...add $4$ to each side. $ x-4+4=\pm 2+4\qquad$ ...simplify. $x=4\pm 2$
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