x squared -x-12=0

x^{2 }- x - 12 = 0

There are 3 ways to solve this problem - factoring, graphing, or the quadratic equation. Factoring is usually the quickest way if you have practice factoring.

We want to re-write this as (x + ?)(x - ?) = 0

The last term of the left side is -12. The only way to get a negative with multiplication is a positive times a negative. I need 2 numbers which multiply to give me -12, but they also have to add up to -1 to give me the -x in the middle (-1x , the invisible 1).

4 and 3 work, but one has to be negative. 4 + -3 = 1, so that is no good, but -4 + 3 = -1 that works!

So we have (x + 3)(x - 4) = 0

Now this equation would be true if x + 3 = 0. It would also be true if x - 4 = 0, so we have to try BOTH.

x + 3 = 0 solves to give you x = -3.

x - 4 = 0 solves to give you x = 4. Therefore your solution is x = -3 and x = 4.