Answer
$x=16$
Work Step by Step
We solve by factoring:
$x+\sqrt{x}=20$
$x+\sqrt{x}-20=0$
$[\sqrt{x}+5][\sqrt{x}-4]=0$
$\sqrt{x}+5=0$ or $\sqrt{x}-4=0$
$\sqrt{x}=-5$ or $\sqrt{x}=4$
$x=(-5)^2$ or $x=4^2$
$x=25$ or $x=16$
However, $x=25$ does not work in the original equation, so we throw this solution out.
$25+\sqrt{25}\ne 20$
Thus, the only solution is: $x=16$