#### Answer

$x=8$

#### Work Step by Step

$x-\sqrt{2x}=4$
Take the $4$ to the left side of the equation and $\sqrt{2x}$ to the right side:
$x-4=\sqrt{2x}$
Square both sides of the equation:
$(x-4)^{2}=(\sqrt{2x})^{2}$
$x^{2}-8x+16=2x$
Take the $2x$ to the left side of the equation and simplify it by combining like terms:
$x^{2}-8x-2x+16=0$
$x^{2}-10x+16=0$
Solve this equation by factoring:
$(x-8)(x-2)=0$
Set both factors equal to $0$ and solve each individual equation:
$x-8=0$
$x=8$
$x-2=0$
$x=2$
Check your answers by substituting them into the original equation:
$x=8$
$8-\sqrt{2(8)}=4$
$4=4$ True
$x=2$
$2-\sqrt{2(2)}=4$
$0\ne4$ False
The final answer is $x=8$