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Simplifying -2k3 + 4k2 + -4k = 0 Reorder the terms: -4k + 4k2 + -2k3 = 0 Solving -4k + 4k2 + -2k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2k'. 2k(-2 + 2k + -1k2) = 0 Ignore the factor 2.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 '(-2 + 2k + -1k2)' equal to zero and attempt to solve: Simplifying -2 + 2k + -1k2 = 0 Solving -2 + 2k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -2k + k2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -2k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2k + k2 = 0 + -2 -2k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2k + k2 = -2 The k term is -2k. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2k + 1 + k2 = -2 + 1 Reorder the terms: 1 + -2k + k2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2k + k2 = -1 Factor a perfect square on the left side: (k + -1)(k + -1) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {0}
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