Answer
$x=16$
Work Step by Step
We are given:
$\sqrt{x}-\sqrt{x-12}=2$
$\sqrt{x}=2+\sqrt{x-12}$
We square both sides:
$(\sqrt{x})^{2}=(2+\sqrt{x-12})^{2}$
$(\sqrt{x})^{2}=(2+\sqrt{x-12})(2+\sqrt{x-12})$
And distribute:
$x=4+4\sqrt{x-12}+(x-12)$
And combine like terms:
$x-x=4-12+4\sqrt{x-12}$
$0=-8+4\sqrt{x-12}$
$8=4\sqrt{x-12}$
$2=\sqrt{x-12}$
We square both sides again:
$2^{2}=(\sqrt{x-12})^{2}$
$4=x-12$
$x=16$
