Answer
$s=-1$.
Work Step by Step
The given expression is
$\Rightarrow s=\sqrt{s+2}$
Square both sides.
$\Rightarrow s^2=(\sqrt{s+2})^2$
Simplify.
$\Rightarrow s^2=s+2$
Move all terms to the left hand side.
$\Rightarrow s^2-s-2=0$
Write the middle term $-s$ as $-2s+s$.
$\Rightarrow s^2-2s+s-2=0$
Factor out common terms.
$\Rightarrow s(s-2)+1(s-2)=0$
Factor out $(s-2)$.
$\Rightarrow (s-2)(s+1)=0$
Use zero product property.
$s-2=0$ or $s+1=0$
Solve for $s$.
$s=2$ or $s=-1$
Check $s=2$.
$\Rightarrow 2=\sqrt{2+2}$
$\Rightarrow 2=\sqrt{4}$
$\Rightarrow 2=2$
Check $s=-1$.
$\Rightarrow -1=\sqrt{-1+2}$
$\Rightarrow -1=\sqrt{1}$
$\Rightarrow -1=1$ which is not true.
Hence, the extraneous solution is $s=-1$.
