Solve x^2 + x -12= 0 for all values of x.

This is a quadratic equation so there are two main methods you can use to solve it- factorising and completing the square.

My preferred method and the one I will demonstrate is factorisation.

The above equation will take the form:

(x + a)(x +b) = 0

Therefore if we multiply out the brackets we get:

x^2 + (a+b)x +ab = 0

This means that

(a+b) = 1 (the coefficient of x)

and 

ab = 12

From trial and error we find the values for a and b which are 

a= -3

b= 4

So x^2 + x -12= 0 can be written as (x-3)(x+4)= 0

When we multiply by 0 we get 0 therefore

x-3 = 0 or 

x+4= 0

From rearranging the above equations we find the answer is x = 3 or x = -4