Question 36455
Although you don't say so, it looks like you are tryng to derive the quadratic formula. Starting with the genaeral form of the quadratic equation:
{{{ax^2+bx+c = 0}}} Subtract c from each side.
{{{ax^2 + bx = -c}}} Divide each side by a.
{{{x^2 + bx/a = -c/a}}} Add the square of half the x-coefficient to each side, that's {{{(b/2a)^2 = b^2/4a^2}}}
{{{x^2 + bx/a + b^2/4a^2 = b^2/4a^2 - c/a}}} Write the left side as a perfect square binomial.
{{{(x + b/2a)^2 = b^2/4a^2 - c/a}}} Use a common denominator to express the right side as a single fraction.
{{{(x + b/2a)^2 = (b^2 - 4ac)/4a^2}}} Take the square root of each side.
{{{x + b/2a = (sqrt(b^2 - 4ac))/2a}}} Subtract {{{b/2a}}} from each side.
{{{x = -b/2a +-sqrt(b^2 - 4ac)/2a}}} Simplify.
{{{x = (-b +- sqrt(b^2 - 4ac))/2a}}}