Answer
$\{2\}$
Work Step by Step
Step 1. Given the equation $\sqrt {8-2x}-x=0, x\leq4$, rewrite the equation as $\sqrt {8-2x}=x$. Take square on both sides to get $8-2x=x^2$ or $x^2+2x-8=0$ which can be factored as $(x+4)(x-2)=0$
Step 2. Solve the above equation to get $x= 2$ (discard $x=-4$ as it is not an answer) or in set form as $\{2\}$
