Answer
$x=4$
Work Step by Step
We solve by factoring:
$x+\sqrt{x}=6$
$x+\sqrt{x}-6=0$
$[\sqrt{x}+3][\sqrt{x}-2]=0$
$\sqrt{x}+3=0$ or $\sqrt{x}-2=0$
$\sqrt{x}=-3$ or $\sqrt{x}=2$
$x=(-3)^2$ or $x=2^2$
$x=9$ or $x=4$
However, $x=9$ does not work in the original equation, so we throw this solution out.
$9+\sqrt{9}\ne 6$
Thus, the only solution is: $x=4$