Where does the quadratic formula come from?

First take the general form of a quadratic equation, ax^2+bx+c=0, this can be written in completed square form, (x+b/2a)^2-(b/2a)^2+c/a=0, rearranging gives, x=-b/2a +/-(b^2/4a^2-c/a)^1/2, which can be written as x=-b/2a +/-((b^2-4ac)/4a^2)^1/2, removing a factor of 1/4a^2=(1/2a)^2, gives, x=-b/2a +/-1/2a(b^2-4ac)^1/2=(-b +/-(b^2-4ac)^1/2)/2a, as required.