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Simplifying 8k3 + -162k = 0 Reorder the terms: -162k + 8k3 = 0 Solving -162k + 8k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2k'. 2k(-81 + 4k2) = 0 Factor a difference between two squares. 2k((9 + 2k)(-9 + 2k)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(9 + 2k)' equal to zero and attempt to solve: Simplifying 9 + 2k = 0 Solving 9 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2k = 0 + -9 2k = 0 + -9 Combine like terms: 0 + -9 = -9 2k = -9 Divide each side by '2'. k = -4.5 Simplifying k = -4.5Subproblem 3
Set the factor '(-9 + 2k)' equal to zero and attempt to solve: Simplifying -9 + 2k = 0 Solving -9 + 2k = 0 Move all terms containing k to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2k = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2k = 0 + 9 2k = 0 + 9 Combine like terms: 0 + 9 = 9 2k = 9 Divide each side by '2'. k = 4.5 Simplifying k = 4.5Solution
k = {0, -4.5, 4.5}
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