How do you factorise the following quadratic: x^2 - 5*x - 14?

An example of an application of factorising quadratics is to find the unknown in the equation, x. Factorising means writing the above equation in the form (x+a)(x+b)=0 Using FOIL (First, Outer, Inner, Last) to expand the brackets we get the equation: x^2+(a+b)x+ab=0 which we can see is in the same format as the expression given. Factorising is just the reverse of expanding the brackets. So we need to find the variables a and b. As we can see from our expanded standard equation the coefficient of the second term is a+b and the coefficient of the last term is a*b. So we need to find two numbers that add together to make 5 and multiply to make negative 14. Lets start with the factors of -14 which are: -1 and 14 -2 and 7 1 and -14 2 and -7 2 and -7 added together make -5 so these are a and b. So we write them into the equation: (x+2)(x-7)=0. And this is our answer.