Question 6637
One of the methods of solving quadratic equations is known as "completing the square".

This method entails making a perfect square trinomial from the given quadratic equation or expression, then factoring the perfect square trinomial into its two identical factors.

This is best demonstrated by illustration:

Starting with your quadratic equation:
{{{x^2 + 4x - 12 = 0}}}

1) Move the constant to the right side of the equation, i.e. add 12 to both sides.
{{{x^2 + 4x = 12}}}

2) Add a new constant that is the square of one-half of the x-coefficient.
{{{((1/2)(4))^2 = 4}}} to both sides.
{{{x^2 + 4x + 4 = 16}}}

3) Factor the trinomial.
{{{(x + 2)(x + 2) = 16}}} or
{{{(x + 2)^2 = 16}}}

Now take the square root of both sides.
{{{sqrt((x + 2)^2) = (+- sqrt(16))}}}
x + 2 = +/-4  Subtract 2 from both sides.

x = 4 - 2 = 2 or
x = -4 -2 = -6

In this case the roots are real.