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: 23


The solutions are $5\sqrt{2}$ and $-5\sqrt{2}$.

Work Step by Step

$ a^{2}=50\qquad$ ...take square roots of each side. $\sqrt{a^{2}}=\sqrt{50}$ ...When solving an equation of the form $x^{2}=s$ where $s>0$, we find both the positive and negative solutions. $ a=\pm\sqrt{50}\qquad$ ...rewrite $50$ as a product of two factors so that one factor is a perfect square. ($50=25\cdot 2$) $ a=\pm\sqrt{25\cdot 2}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ $ a=\pm\sqrt{25}\cdot\sqrt{2}\qquad$ ...evaluate $\sqrt{25} $ ($\sqrt{25}=5$) $a=\pm 5\sqrt{2}$
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