quadratic formula (thing)

The proof of the quadratic equation is delightfully simple to learn. It's also the only proof I had to memorise for College Algebra:

                   Start with: ax2 + bx + c = 0

                   Subtract c: ax2 + bx = -c

                  Divide by a: x2 + bx/a = -c/a

          Complete the Square: x2 + bx/a + b2/4a2 = -c/a + b2/4a2

   Factor left, combine right: (x+b/2a)2 = (b2-4ac)/4a2

                  SQRT it all: x+b/2a = ±SQRT(b2-4ac)/2a

Subtract b/2a from both sides: x = [-b ±SQRT(b2-4ac)]/2a

Sometimes called the quadratic formula. (Probably a better name since it's used to solve quadratic equations.)