# How do you solve sqrt(5x) = -5 and find any extraneous solutions?

Jan 25, 2017

• If $t \ge 0$ then $\sqrt{t} \ge 0$
• If $t < 0$ then $\sqrt{t} = i \sqrt{- t}$ is a pure imaginary number with positive imaginary part.
So $\sqrt{5 x} = - 5$ has no solutions.