Sometime back when trying to work out how to solve $ax^2 - by^2 + cx - dy + e = 0$ I learned that the way to solve such forms is to 'square the terms' and give it the form $A^2 - B^2 - E = 0$, $A = ax + c/2$, $B = by + d/2$, $E = -e + (c/2)^2 + (d/2)^2$.
However I am not able to work out how to square the following equation - $ax^2 + bxy + cx + dy + e = 0$. I guessing I need to transform x and y to x' and y' such that the coefficient of $x'*y'$ is reduced to 0, but not sure how to do this.
Please help or advise.
Thanks!