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Simplifying 0 = 3k * k + k Multiply k * k 0 = 3k2 + k Reorder the terms: 0 = k + 3k2 Solving 0 = k + 3k2 Solving for variable 'k'. Remove the zero: -1k + -3k2 = k + 3k2 + -1k + -3k2 Reorder the terms: -1k + -3k2 = k + -1k + 3k2 + -3k2 Combine like terms: k + -1k = 0 -1k + -3k2 = 0 + 3k2 + -3k2 -1k + -3k2 = 3k2 + -3k2 Combine like terms: 3k2 + -3k2 = 0 -1k + -3k2 = 0 Factor out the Greatest Common Factor (GCF), '-1k'. -1k(1 + 3k) = 0 Ignore the factor -1.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 + 3k)' equal to zero and attempt to solve: Simplifying 1 + 3k = 0 Solving 1 + 3k = 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 + 3k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3k = 0 + -1 3k = 0 + -1 Combine like terms: 0 + -1 = -1 3k = -1 Divide each side by '3'. k = -0.3333333333 Simplifying k = -0.3333333333Solution
k = {0, -0.3333333333}
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