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Simplifying 36k4 + -18k2 = 0 Reorder the terms: -18k2 + 36k4 = 0 Solving -18k2 + 36k4 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '18k2'. 18k2(-1 + 2k2) = 0 Ignore the factor 18.Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve: Simplifying k2 = 0 Solving k2 = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k2 = 0 Take the square root of each side: k = {0}Subproblem 2
Set the factor '(-1 + 2k2)' equal to zero and attempt to solve: Simplifying -1 + 2k2 = 0 Solving -1 + 2k2 = 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 + 2k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2k2 = 0 + 1 2k2 = 0 + 1 Combine like terms: 0 + 1 = 1 2k2 = 1 Divide each side by '2'. k2 = 0.5 Simplifying k2 = 0.5 Take the square root of each side: k = {-0.707106781, 0.707106781}Solution
k = {0, -0.707106781, 0.707106781}
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