(x)squared-8x-16=1

Question

x²-8x-16=1

Answer 1

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

x² - 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(b² - 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.