# Chapter 7 - Section 7.6 - Solving Equations with Radicals - 7.6 Exercises: 20

$x=16$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To solve the given radical equation, $2\sqrt{x}=\sqrt{5x-16} ,$ 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( 2\sqrt{x} \right)^2=\left( \sqrt{5x-16} \right)^2 \\\\ 4x=5x-16 .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} 4x-5x=-16 \\\\ -x=-16 \\\\ x=16 .\end{array} Upon checking, $x=16$ satisfies the original equation.

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