x^2 - x - 90 = 0. Solve to find x.

Comparing to this to ax^2 + bx + c = 0, you'll find that a=1, b=-1, c=90. You need to split b (in this case -1), into two numbers that add up to b (-1), and multiply to ac (90). -> These are -10 and 9. Now, split bx accordingly.. x^2 - 10x + 9x - 90 = 0 (Note, that the order doesn't matter) Look at the first two terms, and factorise (i.e. take out what's common) and do the same with the latter two. x(x-10) + 9(x-10) = 0 As you can see, the same variable is found in both brackets. You can now join the two terms outside the brackets to make (x+9)(x-10) = 0 Which values of x will make either bracket = 0? -> x = -9, x = 10