Derive from the standard quadratic equation, the form of the quadratic solution

ax²+bx+c=0 : basic quadratic equation

a(x² + bx/a) + c=0  

a((x+b/2a)² - b²/4a²) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b²/4a^2, )

a(x+b/2a)² - b²/4a + c= 0 (a cancels 4a² to make 4a)

a(x+b/2a)² = (b²-4ac)/4a  (rewrite b²/4a - c)

(x+b/2a)² = (b²-4ac)/4a²

(x+b/2a) = +/-(rootof(b²-4ac))/2a  (square root gives +/- answers

x= (-b +/- (rootof(b²-4ac)))/2a  (x term singled out and the quadratic soln is written)