Solve for $m$ in $(-3m)^2=4p-8$

Question

So, usually when I finish answering a question in my book, I peek at the answers.

It seems like I'm (for me at least) unexplainably incorrect.

The question is to solve $m$ in $(-3m)^2=4p-8$

My working is as follows:

$$(-3m)^2=4p-8$$ $$9m^2=4p-8$$ $$m^2=\frac {4p-8}{9}$$ $$m=\sqrt\frac{4p-8}{9}$$

But the book states that the answer is $m =-\sqrt\frac{4p-8}{9}$

Why is the answer a negative?

Answer 1

HINT: $$m=\pm\sqrt{\frac{4p-8}{9}}$$ is only true if $$4p-8\geq 0$$ if $m$ is real