Question

Solve using the quadratic formula.

7k2 − 4k − 8 = 0

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

k =
or k =

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the quadratic equation 7k^2 - 4k - 8 = 0 using the quadratic formula, we first identify the coefficients a, b, and c in the equation.

a = 7
b = -4
c = -8

Next, we plug these values into the quadratic formula:
k = (-(-4) ± √((-4)^2 - 4(7)(-8))) / (2(7))
k = (4 ± √(16 + 224)) / 14
k = (4 ± √240) / 14

Now, simplify the radical:
k = (4 ± √240) / 14
k = (4 ± 4√15) / 14

Therefore, the solutions are:
k = (4 + 4√15) / 14
k = (4 - 4√15) / 14

These can be further simplified if necessary.