Solve the quadratic equation: x^2 - 2x - 15 = 0
To solve this, you need to find two factors of -15 that total to give -2. The solution we're looking for is of the for (x + something) (x + something)=0, as you can then solve each bracket to get two results for x.Since the 'c' part (remember Ax2 + Bx + C = 0 is the general equation) is negative, we know one factor minus another equals 2. What factors of 15 are there? Well, there aren't many; 1,3,5,15 are the only ones. 5-3 gives us 2, which is what we want!If we had 5 and -3 to replace the two 'something's in our solution, we would have a total of 2x. But we want -2x, so we must use -5 and +3 in our solution. Then, we have (x-5)(x+3)=0. Almost done!As each bracket must =0, as they multiply to give 0, we know x-5=0 and x+3=0. Solving those gives x=5 and x=-3; done!
