Answer
$9$.
Work Step by Step
The given function is
$\Rightarrow f(x)= \sqrt {x+16}-\sqrt x-2$
Plug $f(x)=0$ into the equation.
$\Rightarrow 0= \sqrt {x+16}-\sqrt x-2$
Add $\sqrt x+2$ to both sides.
$\Rightarrow 0+\sqrt x+2= \sqrt {x+16}-\sqrt x-2+\sqrt x+2$
Simplify.
$\Rightarrow \sqrt x+2= \sqrt {x+16}$
Square both sides.
$\Rightarrow (\sqrt x+2)^2= (\sqrt {x+16})^2$
Use the special formula $(A-B)^2=A^2-2AB+B^2$
We have $A=\sqrt x$ and $B=2$
$\Rightarrow (\sqrt x)^2+2(\sqrt x)(2)+(2)^2=x+16$
Simplify.
$\Rightarrow x+4\sqrt x+4=x+16$
Add $-x-4$ to both sides.
$\Rightarrow x+4\sqrt x+4-x-4=x+16-x-4$
Simplify.
$\Rightarrow 4\sqrt x=12$
Divide both sides by $4$.
$\Rightarrow \frac{4\sqrt x}{4}=\frac{12}{4}$
Simplify.
$\Rightarrow \sqrt x=3$
Square both sides.
$\Rightarrow (\sqrt x)^2=(3)^2$
Simplify.
$\Rightarrow x=9$
The $x-$ intercept is $9$.
