#### Answer

$x=16$

#### Work Step by Step

$x-2\sqrt{x}=8$
Take the $8$ to the left side of the equation and the $2\sqrt{x}$ to the right side:
$x-8=2\sqrt{x}$
Square both sides of the equation:
$(x-8)^{2}=(2\sqrt{x})^{2}$
$x^{2}-16x+64=4x$
Take the $4x$ to the left side of the equation and simplify it by combining like terms:
$x^{2}-16x-4x+64=0$
$x^{2}-20x+64=0$
Solve this equation by factoring:
$(x-16)(x-4)=0$
Make both factor equal to $0$ and solve each individual equation:
$x-16=0$
$x=16$
$x-4=0$
$x=4$
Check the answers by substituting them into the original equation:
$x=16$
$16-2\sqrt{16}=8$
$8=8$ True
$x=4$
$4-2\sqrt{4}=8$
$0\ne8$ False
The final solution is $x=16$