## Intermediate Algebra (12th Edition)

Published by Pearson

# Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises: 25

#### Answer

$x=\{ -7,3 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $(x+2)^2=25 ,$ take the square root of both sides (Square Root Property) and simplify the resulting radical. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} x+2=\pm\sqrt{25} .\end{array} Simplifying the radical and using the properties of equality to isolate the variable result to \begin{array}{l}\require{cancel} x+2=\pm5 \\\\ x=-2\pm5 .\end{array} The solutions are \begin{array}{l}\require{cancel} x=-2-5 \\\\ x=-7 \\\\\text{OR}\\\\ x=-2+5 \\\\ x=3 .\end{array} Hence, $x=\{ -7,3 \} .$

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