Answer
$x=6$
Work Step by Step
Square both sides and put all terms on one side to create a quadratic equation. Then use trial and error to factor it, and set the values found equal to zero. One of the solutions does not work.
$\sqrt {x+10}=x-2$
$(\sqrt {x+10})^2=(x-2)^2$
$x+10=x^2-4x+4$
$x^2-5x-6=0$
$(x+1)(x-6)=0$
$x=-1,6$
$\sqrt {-1+10}\ne-1-2$
$x=6$
