Verified answer

that problem looks like a prime, because the factors of -5 to not equal the sum of -13.

With a 5, I'll use multiples of 5 for my guesses.

x = 5 f(x) = 25 - 65 - 5 = - 45: no good

x = 10 f(10) = 100 - 130 - 5 = - 25: no good, but closer to zero.

x = 15 f(15) = 225 - 195 - 5 = 25: no good, but I've passed a root.

Time to break out the quadratic formula, where a = 1, b = - 13, c = - 5.

x = 13/2 +/- sqrt(189)/2

f(x) = x^2 – 13x – 5 = 0

Plug it into the quadratic formula:

x = (-b +or- sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -13 and c = -5

Your answers will be:

x = (1/2)*(13 +or- 3sqrt(21))