Question 428435
Start with the general form {{{ax^2 + bx + c = 0}}} and divide both sides by {{{a}}} to get {{{x^2 + (b/a)x + (c/a) = 0}}}. To complete the square, we want the constant term to be {{{(b/2a)^2}}} or {{{b^2/4a^2}}} so we add {{{b^2/4a^2 - c/a}}} to both sides to get


{{{x^2 + (b/a)x + b^2/4a^2 = b^2/4a^2 - c/a = (b^2 - 4ac)/4a^2}}}. The left side factors to {{{(x - b/2a)^2}}} so the equation is equivalent to


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


Taking square root of both sides,


{{{x + b/2a = (0 +- sqrt(b^2 - 4ac))/2a}}}

{{{x = (-b +- sqrt(b^2 - 4ac))/2a}}} <-- and there's the quadratic formula.