Answer
There is no extraneous solution.
Work Step by Step
The given equation is
$\Rightarrow -3g=\sqrt{-18-27g}$
Check $g=-2$.
$\Rightarrow -3g=\sqrt{-18-27g}$
$\Rightarrow -3(-2)=\sqrt{-18-27(-2)}$
$\Rightarrow 6=\sqrt{-18+54}$
$\Rightarrow 6=\sqrt{36}$
$\Rightarrow 6=6$
True.
Check $g=-1$.
$\Rightarrow -3g=\sqrt{-18-27g}$
$\Rightarrow -3(-1)=\sqrt{-18-27(-1)}$
$\Rightarrow 3=\sqrt{-18+27}$
$\Rightarrow 3=\sqrt{9}$
$\Rightarrow 3=3$
True.
Hence, there is no extraneous solution.
