Answer
$x=0$
Work Step by Step
We solve by factoring:
$x+8\sqrt{x}=0$
$8\sqrt{x}=-x$
$(8\sqrt{x})^{2}=(-x)^{2}$
$64x=x^{2}$
$x^{2}-64x=0$
$x(x-64)=0$
$x=0$ or $x=64$
However, $x=64$ does not work the original equation, so we throw this solution out.
$(64)+8\sqrt{64}\ne 0$
Thus, the only solution is: $x=0$