Solve x^2 + 2x = 48 for all values of x

First we need to rearrange so that it's all on one side of the equals sign:x² + 2x - 48 = 0 Now we have to find what will sum to make the coefficient of x (2) and multiplies together to get -48. So, the factors of 48 are 48 & 1, 24 & 2, 16 & 3, 12 & 4, 8 & 6. As 48 is negative (-) one of the numbers in the pairs must be negative, so in order to make 2 (coefficient of x) the only possible pair is 8 and -6 added together. Therefore; x² + 2x - 48 = (x + 8)(x - 6) = 0And so; x can be either (-)8 or (+)6 in order to make the equation true.