Question

How is the quadratic formula derived from the quadratic equation?

Answer 1

ax^2 + bx + c = 0

a(x^2 + b/a x) = -c
x^2 + b/a x = -c/a
x^2 + b/a x + (b/2a)^2 = (b/2a)^2 - c/a
(x + b/2a)^2 = b^2/4a^2 - c/a
(x + b/2a)^2 = (b^2-4ac)/4a^2
x + b/2a = ±√(b^2-4ac)/2a
x = [-b±√(b^2-4ac)]/2a