X is random variable with mean 44.584 and sd 89.265. What non zero value maust a take so that random variable given by Y=aX + a^2 has its mean equal to its sd?

I get 44.681 but am not sure if method is correct:

E(Y) = a*mean + a^2

V(Y) = a^2*sd^2

and then equate them.

Is this right?