How do you solve a quadratic equation e.g. x^2 - 5x - 14 = 0?

Quadratic equations take the form ax^2 + bx + c = 0. In the case above, a = 0, b = -5, c = -14. In order to solve it, we can factorise the equation into the form (x+c)(x+d) = 0. The answers are then x = -c, x = -d. There are 2 possible solutions because a quadratic curve often crosses the x axis twice, giving 2 possible solutions. The trick to finding c and d are that they must add together to give b (-5 for the case above) and multiply together to give c (-14 in the case above). Here we find that c is -7 and d is 2, these add to give -5 and multiply to give -14. Therefore, the equation can also be written as (x-7)(x+2) = 0. Our solutions are then, x=7, x= -2. We can then substitute these for x and check to see if it works.