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Simplifying 8k2 + 16k + -15 = 9 Reorder the terms: -15 + 16k + 8k2 = 9 Solving -15 + 16k + 8k2 = 9 Solving for variable 'k'. Reorder the terms: -15 + -9 + 16k + 8k2 = 9 + -9 Combine like terms: -15 + -9 = -24 -24 + 16k + 8k2 = 9 + -9 Combine like terms: 9 + -9 = 0 -24 + 16k + 8k2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + 2k + k2) = 0 Factor a trinomial. 8((-3 + -1k)(1 + -1k)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-3 + -1k)' equal to zero and attempt to solve: Simplifying -3 + -1k = 0 Solving -3 + -1k = 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 + -1k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1k = 0 + 3 -1k = 0 + 3 Combine like terms: 0 + 3 = 3 -1k = 3 Divide each side by '-1'. k = -3 Simplifying k = -3Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 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 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1Solution
k = {-3, 1}
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