x^{2}-8x-16=1

First, you need to subtract one from each side so the expression equals zero. When you do this the equation becomes

x^{2} - 8x - 17 = 0

17 is a prime number, so its only two factors are 17 and 1. Can you find a case where two factors will sum to -8? -17 + 1 is -16, and 17 + (-1) = 16. Thus, we'll have to solve for the roots of this quadratic equation using

x = [ -b +- sqrt(b^{2} - 4ac) ]/(2a)

The three variables for this equation come from the quadratic expression we are solving:

a = 1, b = -8, and c = -17

If you substitute and solve, you will get the answers x = (4 +- sqrt(33) ). Substitute these into the original question and you'll find these two answers satisfy the equation.