Completing the Square

The conversion of an equation of the form $ax^2+bx+c$ to the form

$$a\left({x + {b\over 2a}}\right)^2+\left({c - {b^2\over 4a}}\right),$$

which, defining $B\equiv b/2a$ and $C\equiv c-b^2/4a$, simplifies to

$$a(x+B)^2+C.$$