Answer
$x=9$
Work Step by Step
Isolating the radical and then squaring both sides, the solution/s of the given equation, $
x-\sqrt{x}-6=0
,$ is/are
\begin{array}{l}\require{cancel}
x-6=\sqrt{x}
\\\\
(x-6)^2=(\sqrt{x})^2
\\\\
(x)^2+2(x)(-6)+(-6)^2=x
\\\\
x^2-12x+36=x
\\\\
x^2-13x+36=0
\\\\
(x-9)(x-4)=0
\\\\
x=\{4,9\}
.\end{array}
Upon checking, only $
x=9
$ satisfies the original equation.
