Question 80201
Starting with:{{{ax^2+bx+c = 0}}} complete the square and see what results.
{{{ax^2+bx+c = 0}}} Subtract c from both sides..
{{{ax^2+bx = -c}}} Next, divide through by a.
{{{x^2+(b/a)x = -c/a}}} Now complete the square in the x-terms by adding the square of half the x-coefficient to both sides.. This would be{{{(b/2a)^2 = b^2/4a^2}}}
{{{x^2+(b/a)x+b^2/4a^2 = b^2/4a^2-c/a}}} Now factor the left side.
{{{(x+b/2a)^2 = b^2/4a^2-c/a}}} Simplify the right side.
{{{(x+b/2a)^2 = (b^2-4ac)/4a^2}}} Now take the square root of both sides.
{{{x+b/2a = sqrt((b^2-4ac)/4a^2)}}} Simplify.
{{{x+b/2a = sqrt(b^2-4ac)/2a}}} Finally, subtract {{{b/2a}}} from both sides.
{{{x = (-b/2a)+-sqrt(b^2-4ac)/2a}}} Simplify.
{{{x = (-b+-sqrt(b^2-4ac))/2a}}} Does this look familiar?
If you don't recognise it, it's the quadratic formula!