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Simplifying 5k10 + -5k6 = 0 Reorder the terms: -5k6 + 5k10 = 0 Solving -5k6 + 5k10 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5k6'. 5k6(-1 + k4) = 0 Factor a difference between two squares. 5k6((1 + k2)(-1 + k2)) = 0 Factor a difference between two squares. 5k6((1 + k2)((1 + k)(-1 + k))) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'k6' equal to zero and attempt to solve: Simplifying k6 = 0 Solving k6 = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + k2)' equal to zero and attempt to solve: Simplifying 1 + k2 = 0 Solving 1 + k2 = 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 + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k2 = 0 + -1 k2 = 0 + -1 Combine like terms: 0 + -1 = -1 k2 = -1 Simplifying k2 = -1 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 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 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 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1Subproblem 4
Set the factor '(-1 + k)' equal to zero and attempt to solve: Simplifying -1 + k = 0 Solving -1 + k = 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 + k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + k = 0 + 1 k = 0 + 1 Combine like terms: 0 + 1 = 1 k = 1 Simplifying k = 1Solution
k = {-1, 1}
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