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Simplifying 9k3 = 4k Solving 9k3 = 4k Solving for variable 'k'. Reorder the terms: -4k + 9k3 = 4k + -4k Combine like terms: 4k + -4k = 0 -4k + 9k3 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(-4 + 9k2) = 0 Factor a difference between two squares. k((2 + 3k)(-2 + 3k)) = 0Subproblem 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 '(2 + 3k)' equal to zero and attempt to solve: Simplifying 2 + 3k = 0 Solving 2 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3k = 0 + -2 3k = 0 + -2 Combine like terms: 0 + -2 = -2 3k = -2 Divide each side by '3'. k = -0.6666666667 Simplifying k = -0.6666666667Subproblem 3
Set the factor '(-2 + 3k)' equal to zero and attempt to solve: Simplifying -2 + 3k = 0 Solving -2 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3k = 0 + 2 3k = 0 + 2 Combine like terms: 0 + 2 = 2 3k = 2 Divide each side by '3'. k = 0.6666666667 Simplifying k = 0.6666666667Solution
k = {0, -0.6666666667, 0.6666666667}
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