How to derive the quadratic formula by completing the square.

Question

Derive the quadratic formula from ax² + bx + c = 0 by completing the square.

Answer 1

Divide by a.

x² + (b/a) x + (c/a) = 0

(x- (b/2a))² - (b²/4a²) + (c/a) = 0

(x - (b/2a))² = b²/4a² - c/a = (b² - 4ac) / 4a²

x - (b/2a) = +/- sqrt (b²-4ac) / 2a

x = [ - b +/- sqrt (b² - 4ac) ] / 2a, the quadratic formula

^Mike