Answer
$x=9$
Work Step by Step
The given equation is
$\Rightarrow \sqrt{2x-9}=\sqrt{x}$
Square each side of the equation.
$\Rightarrow (\sqrt{2x-9})^2=(\sqrt{x})^2$
Simplify.
$\Rightarrow 2x-9=x$
Add $9-x$ to each side.
$\Rightarrow 2x-9+9-x=x+9-x$
Simplify.
$\Rightarrow x=9$
Check $x=9$.
$\Rightarrow \sqrt{2(9)-9}=\sqrt{9}$
$\Rightarrow \sqrt{18-9}=\sqrt{9}$
$\Rightarrow \sqrt{9}=\sqrt{9}$
True.
Hence, the solution is $x=9$.
