College Algebra

Question

Derive the Quadratic Formula by completing the square ax^2+bx+c=0

Answer 1

a standard quadratic is

ax^2 + bx + c = 0

divide by a

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

add (b/2a)^2 to both sides

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

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

x+b/2a = (1/2a)sqr(b^2 - 4ac)

x = -b/2a + or - (1/2a)sqr(b^2 - 4ac)

x = [-b + or - sqr(b^2 - 4ac)]/2a