Solve using the quadratic formula.
k2 − 8k − 1 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
k =
or k =
Using the quadratic formula:
k = [ 8 ± √(8² - 4(1)(-1)) ] / 2(1)
k = [ 8 ± √(64 + 4) ] / 2
k = [ 8 ± √68 ] / 2
k = [ 8 ± 8.25 ] / 2
k = (8 + 8.25) / 2
k = 16.25 / 2
k = 8.125
or
k = (8 - 8.25) / 2
k = -0.25 / 2
k = -0.125
So, the solutions are:
k = 8.125 or k = -0.125