Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.5 - Solving Radical Equations - Problem Set 9.5 - Page 424: 28

Answer

$x=-2$

Work Step by Step

Squaring both sides of the equation and then using the properties of equality, we obtain: \begin{array}{l}\require{cancel}\left( \sqrt{-2x} \right)^2=\left( x+4 \right)^2 \\\\ -2x=(x)^2+2(x)(4)+(4)^2 \\\\ -2x=x^2+8x+16 \\\\ 0=x^2+(8x+2x)+16 \\\\ x^2+10x+16=0 \\\\ (x+8)(x+2)=0 \\\\ x=\{-8,-2\} .\end{array} Upon checking, only $ x=-2 $ satisfies the original equation.
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