Solve the quadratic equation x^2 - 5x - 14 = 0, using factorisation.

Using factorisation, first we would have to look at the factors that multiply to make the last term, (-14). We know that they are +/- 7 and -/+2, and +/- 14 and -/+ 1, respectively. Now we have listed the factors, we have to see which pair adds to make the coefficent of x, which in this case is (-5). From these pairs, only (-7) and (+2) add to make (5).

This means that the quadratic equation factorises to become (x - 7)(x + 2) - notice here that when you multiply out these two brackets, using the FOIL method, you get the equation that you had started with.

Setting (x - 7)(x + 2) = 0, we can now find the roots. One of these brackets have to equal (0) in order for the euqation to be true. Here, we can easily see that setting x = 7 or x = -2 does the trick, and hence (7) and (-2) are roots of the equations.