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Simplifying -16k2 + 8k + 24 = 0 Reorder the terms: 24 + 8k + -16k2 = 0 Solving 24 + 8k + -16k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '8'. 8(3 + k + -2k2) = 0 Factor a trinomial. 8((3 + -2k)(1 + k)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + -2k)' equal to zero and attempt to solve: Simplifying 3 + -2k = 0 Solving 3 + -2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2k = 0 + -3 -2k = 0 + -3 Combine like terms: 0 + -3 = -3 -2k = -3 Divide each side by '-2'. k = 1.5 Simplifying k = 1.5Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Solution
k = {1.5, -1}
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