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: 24


The solutions are $2\sqrt{21}$ and $-2\sqrt{21}$

Work Step by Step

$ x^{2}=84\qquad$ ...take square roots of each side. $\sqrt{x^{2}}=\sqrt{84}$ ...When solving an equation of the form $x^{2}=s$ where $s>0$, we find both the positive and negative solutions. $ x=\pm\sqrt{84}\qquad$ ...rewrite $84$ as a product of two factors so that one factor is a perfect square. ($84=4\cdot 21$) $ x=\pm\sqrt{4\cdot 21}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ $ x=\pm\sqrt{4}\cdot\sqrt{21}\qquad$ ...evaluate $\sqrt{4} $ ($\sqrt{4}=2$) $x=\pm 2\sqrt{21}$
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