Intermediate Algebra (12th Edition)

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

Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 25

Answer

no solution

Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $ x=\sqrt{x^2+3x+9} ,$ square both sides of the equation and then isolate the variable. Finally, do checking of the solution with the original equation. $\bf{\text{Solution Details:}}$ Squaring both sides of the equation results to \begin{array}{l}\require{cancel} \left( x \right)^2=\left( \sqrt{x^2+3x+9} \right)^2 \\\\ x^2=x^2+3x+9 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x^2-x^2-3x=9 \\\\ -3x=9 \\\\ x=\dfrac{9}{-3} \\\\ x=-3 .\end{array} Upon checking, $ x=-3 $ DOES NOT satisfy the original equation. Hence, there is $\text{ no solution .}$
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