Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set: 21

Answer

$x=\{ 0,36 \}$

Work Step by Step

Squaring both sides of the given equation, $ 6\sqrt{x}=x ,$ results to \begin{array}{l}\require{cancel} 6\sqrt{x}=x \\\\ \left( 6\sqrt{x} \right)^2=(x)^2 \\\\ 36x=x^2 \\\\ 0=x^2-36x \\\\ x^2-36x=0 .\end{array} Factoring the $GCF=x,$ the equation above is equivalent to \begin{array}{l}\require{cancel} x^2-36x=0 \\\\ x(x-36)=0 .\end{array} Equating each factor to zero (Zero Product Property), the solutions are \begin{array}{l}\require{cancel} x=0 \\\\\text{OR}\\\\ x-36=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} x=0 \\\\\text{OR}\\\\ x-36=0 \\\\ x=36 .\end{array} Upon checking, both solutions satisfy the original equation. Hence, $ x=\{ 0,36 \} .$
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