So the solution is fairly straight forward as once you get past the fact that it is ok to "guess".
We can see something close with a guess:
(x(sqrt(A))+(B/(2sqrt(A))))^2 = (Ax+Bx + B^2/4A)
then we see a second guess where add in a term
to make things work out like we want.
(x(sqrt(A))+(B/(2sqrt(A))))^2 - (B^2/4A) + C = 0
All in all this is an easy problem now that I am comfortable with shaking the table until the math comes out right. However, I remember epically failing on this problem when I was 13 because I just could not wrap my head around "guessing" or adding new terms where needed.