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: 21

Answer

$x=\pm3\sqrt{3}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given equation, $ 2x^2+7=61 ,$ use the properties of equality and express the equation in the form $x^2=c.$ Then take the square root of both sides (Square Root Property) and simplify the resulting radical. $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} 2x^2=61-7 \\\\ 2x^2=54 \\\\ x^2=\dfrac{54}{2} \\\\ x^2=27 .\end{array} Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} x=\pm\sqrt{27} .\end{array} Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to \begin{array}{l}\require{cancel} x=\pm\sqrt{9\cdot3} \\\\ x=\pm\sqrt{(3)^2\cdot3} \\\\ x=\pm3\sqrt{3} .\end{array}
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