The problem states: x * (x + 5) = 204
Perform the multiplication on the left side: (x * x) + (5 * x) = 204 x * x, x squared, is x^2
Subtract 204 from both sides of the equation: x^2 + 5x - 204 = 204 - 204 = 0
We have x^2 + 5x - 204 = 0
Factor the equation on the left side: (x + a) * (x - b) = 0 a and b used for illustration
One of them has to be negative so we get -204 when they are multiplied together (a * -b) = -204
One of them has to be 5 larger than the other so when we add ax to -bx we get 5x
Factors of 204 that satisfy the requirements are 17 and 12
(x + 17) * (x - 12) = 0
One of the quantities has to be zero to produce a zero from the multiplication
x + 17 = 0 x = -7 a side -7 feet long is not likely in the real world
x - 12 = 0 x = 12
This satisfies the original statement that one side is 5 feet longer than the other; one is 12 feet the other is 17 feet