Using the quadratic formula, find the solutions to `x^{2}-16x-15=0`
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To find the solutions to the quadratic equation `x^2 - 16x - 15 = 0` using the quadratic formula, we can use the formula
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Here, a = 1, b = -16, and c = -15.
Substituting these values into the formula, we have:
x = (-(-16) ± sqrt((-16)^2 - 4(1)(-15))) / (2(1))
Simplifying,
x = (16 ± sqrt(256 + 60)) / 2
x = (16 ± sqrt(316)) / 2
x = (16 ± sqrt(316)) / 2
Taking the square root of 316,
x = (16 ± 2sqrt(79)) / 2
Simplifying further,
x = 8 ± sqrt(79)
Therefore, the solutions to the equation `x^2 - 16x - 15 = 0` are:
x = 8 + sqrt(79)
x = 8 - sqrt(79)