Question 111186
Deriving the quadratic formula:

{{{ax^2+bx+c = 0}}} Divide by a.
{{{x^2+(b/a)x+c/a = 0}}} Subtract c/a from both sides.
{{{x^2+(b/a)x = -c/a}}} Now complete the square in x on the left side by adding the square of half the x-coefficient ({{{(b/2a)^2}}}) to both sides. 
{{{x^2+(b/a)x+(b/2a)^2 = (b/2a)^2-(c/a)}}} Factor the left side.
{{{(x+(b/2a))^2 = (b/2a)^2-(c/a)}}} Take the square root of both sides. You'll have two answers here, + and -
{{{x+b/2a = sqrt((b/2a)^2-(c/a))}}} Simplify the contents of the radical.
{{{x+b/2a = sqrt(b^2/4a^2-c/a)}}} Combine the fractions under the radical over a common denominator ({{{4a^2}}})
{{{x+b/2a = sqrt((b^2-4ac)/4a^2)}}} Take the square root of the denominator.
{{{x+b/2a = (sqrt(b^2-4ac))/2a}}} Subtract {{{b/2a}}} from both sides.
{{{x = (-b/2a)+-sqrt(b^2-4ac)/2a}}} Simplify the right side.
{{{x = (-b+-sqrt(b^2-4ac))/2a}}}