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Simplifying k = 9k(-2k * k + 6) Multiply k * k k = 9k(-2k2 + 6) Reorder the terms: k = 9k(6 + -2k2) k = (6 * 9k + -2k2 * 9k) k = (54k + -18k3) Solving k = 54k + -18k3 Solving for variable 'k'. Combine like terms: k + -54k = -53k -53k + 18k3 = 54k + -18k3 + -54k + 18k3 Reorder the terms: -53k + 18k3 = 54k + -54k + -18k3 + 18k3 Combine like terms: 54k + -54k = 0 -53k + 18k3 = 0 + -18k3 + 18k3 -53k + 18k3 = -18k3 + 18k3 Combine like terms: -18k3 + 18k3 = 0 -53k + 18k3 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(-53 + 18k2) = 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 '(-53 + 18k2)' equal to zero and attempt to solve: Simplifying -53 + 18k2 = 0 Solving -53 + 18k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '53' to each side of the equation. -53 + 53 + 18k2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 18k2 = 0 + 53 18k2 = 0 + 53 Combine like terms: 0 + 53 = 53 18k2 = 53 Divide each side by '18'. k2 = 2.944444444 Simplifying k2 = 2.944444444 Take the square root of each side: k = {-1.715938357, 1.715938357}Solution
k = {0, -1.715938357, 1.715938357}
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