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Simplifying 12k5 + -3k = 0 Reorder the terms: -3k + 12k5 = 0 Solving -3k + 12k5 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3k'. 3k(-1 + 4k4) = 0 Factor a difference between two squares. 3k((1 + 2k2)(-1 + 2k2)) = 0 Ignore the factor 3.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 '(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 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
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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