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Simplifying k3 + k2 + 20k = 0 Reorder the terms: 20k + k2 + k3 = 0 Solving 20k + k2 + k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(20 + k + k2) = 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 '(20 + k + k2)' equal to zero and attempt to solve: Simplifying 20 + k + k2 = 0 Solving 20 + k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + k + -20 + k2 = 0 + -20 Reorder the terms: 20 + -20 + k + k2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + k + k2 = 0 + -20 k + k2 = 0 + -20 Combine like terms: 0 + -20 = -20 k + k2 = -20 The k term is k. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. k + 0.25 + k2 = -20 + 0.25 Reorder the terms: 0.25 + k + k2 = -20 + 0.25 Combine like terms: -20 + 0.25 = -19.75 0.25 + k + k2 = -19.75 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = -19.75 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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