Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.1 - Solving Quadratic Equations by the Square Root Property - Exercise Set - Page 631: 32


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

Work Step by Step

The left side of the given equation, $ x^2+4x+4=25 ,$ is a perfect square trinomial whose factored form is \begin{array}{l}\require{cancel} (x+2)^2=25 .\end{array} Taking the square root of both sides (the Square Root Property), the solutions to the given equation are \begin{array}{l}\require{cancel} x+2=\pm\sqrt{25} \\\\ x+2=\pm\sqrt{(5)^2} \\\\ x=-2\pm5 .\end{array} Hence, $ x=\left\{ -7,3 \right\} .$
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