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: 31


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

Work Step by Step

$ 4(x-1)^{2}=8\qquad$ ...divide each side with $4$. $(x-1)^{2}=2\qquad$ ...take square roots of each side. $\sqrt{(x-1)^{2}}=\sqrt{2}\qquad$ ...simplify. ...When solving an equation of the form $x^{2}=s$ where $s>0$, we find both the positive and negative solutions. $ x-1=\pm\sqrt{2}\qquad$ ...add $1$ to each side. $ x-1+1=\pm\sqrt{2}+1\qquad$ ...simplify. $x=1\pm\sqrt{2}$
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