College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises: 41

Answer

$x=2$

Work Step by Step

$\sqrt{x+2}=x$ $(\sqrt{x+2})^{2}=x^{2}$ $x+2=x^{2}$ $0=x^{2}-x-2$ $x^{2}-x-2=0$ $(x+1)(x-2)=0$ $x+1=0$ or $x-2=0$ $x=-1$ or $x=2$ We need to confirm the solutions. First, we confirm $x=-1$: Left side=$\sqrt{-1+2}=\sqrt{1}=1$ Right side=$-1$ The sides disagree, so $x=-1$ is not a solution. Next, we confirm $x=2$: Left side=$\sqrt{2+2}=\sqrt{4}=2$ Right side=$2$ The sides agree, so $x=2$ is a solution.
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