Question 31789
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{{{ax^2 + bx + c = 0}}} Subtract c from both sides of the equation.
{{{ax^2 + bx = -c}}} Divide both sides by a.
{{{x^2 + (b/a)x = (-c/a)}}} Complete the square in the x-terms by adding the square of half the x-coefficient {{{(b/2a)^2 = b^2/4a^2}}} to both sides.
{{{x^2 + (b/a)x + b^2/4a^2 = (b^2/4a^2) - c/a}}} Factor the left side of the equation.
{{{(x + (b/2a))^2 = b^2/4a^2 - c/a}}} Simplify the right side.
{{{(x + (b/2a))^2 = (b^2 - 4ac)/4a^2}}} Take the square root of both sides.
{{{(x + (b/2a)) = (sqrt(b^2 - 4ac))/2a}}} Subtract{{{b/2a}}} from both sides.
{{{x = (-b/2a) +-sqrt(b^2 - 4ac)/2a}}} Simplify.
{{{x = (-b+-sqrt(b^2 - 4ac))/2a}}}