Answer
$\{16\}$.
Work Step by Step
The given expression is
$\Rightarrow \sqrt{x-7}=7-\sqrt{x}$
Square both sides.
$\Rightarrow (\sqrt{x-7})^2=(7-\sqrt{x})^2$
Use the special formula $(A-B)^2=A^2-2AB+B^2$
We have $A=7$ and $B=\sqrt x$
$\Rightarrow x-7=(7)^2-2(7)(\sqrt x)+(\sqrt{x})^2$
Simplify.
$\Rightarrow x-7=49-14\sqrt x+x$
Add $14\sqrt x-x+7$ to both sides.
$\Rightarrow x-7+14\sqrt x-x+7=49-14\sqrt x+x+14\sqrt x-x+7$
Add like terms.
$\Rightarrow 14\sqrt x=56$
Divide both sides by $14$.
$\Rightarrow \frac{14\sqrt x}{14}=\frac{56}{14}$
Simplify.
$\Rightarrow \sqrt x=4$
Square both sides.
$\Rightarrow (\sqrt x)^2=(4)^2$
Simplify.
$\Rightarrow x=16$
The solution set is $\{16\}$.
