Show proof of deriving the Quadratic Formula from the Quadratic Equation ax^2 + bx + c = O

Answer 1

factor out an a
a(x^2 + b/a) + c = 0

compete the square and don't change the value
a(x^2 + b/a + b^2/4a^2) - a(b^2/4a^2) + c = 0

a(x + b/2a)^2 - b^2/4a + c = 0
(x + b/2a)^2 - b^2/4a^2 + c/a = 0
(x+b/2a)^2 = (b^2 - 4ac)/4a^2
x + b/2a = ±√(b^2-4ac) / 2a
x = (-b ± √(b^2-4ac))/2a