## Intermediate Algebra (6th Edition)

Published by Pearson

# Chapter 7 - Review: 158

#### Answer

$x=4$

#### Work Step by Step

Using the properties of equality, the given equation, $\sqrt{x}+2=x ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{x}=x-2 .\end{array} Raising both sides to the second power, then the solution/s to the equation above is/are \begin{array}{l}\require{cancel} x=(x-2)^2 \\\\ x=(x)^2+2(x)(-2)+(-2)^2 \\\\ x=x^2-4x+4 \\\\ -x^2+(x+4x)-4=0 \\\\ -x^2+5x-4=0 \\\\ x^2-5x+4=0 \\\\ (x-4)(x-1)=0 \\\\ x=\left\{ 1,4 \right\} .\end{array} Upon checking, only $x=4$ satisfies the original equation.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.