Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises: 92

Answer

$x=\pm\sqrt{a^2+36}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the solutions of the given equation, $ x^2-a^2-36=0 ,$ isolate first the squared variable. Then take the square root of both sides ((Square Root Property). $\bf{\text{Solution Details:}}$ Using the properties of equality to isolate $x$, the given equation is equivalent to \begin{array}{l}\require{cancel} x^2-a^2-36=0 \\\\ x^2=a^2+36 .\end{array} Taking the square root of both sides, the equation above is equivalent to \begin{array}{l}\require{cancel} x=\pm\sqrt{a^2+36} .\end{array}
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