Answer
$x=5$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
x=\sqrt{x^2+4x-20}
,$ 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+4x-20} \right)^2
\\\\
x^2=x^2+4x-20
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
x^2-x^2-4x=-20
\\\\
-4x=-20
\\\\
x=\dfrac{-20}{-4}
\\\\
x=5
.\end{array}
Upon checking, $
x=5
$ satisfies the original equation.