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Simplifying 18k3 + -48k2 + 66k = 0 Reorder the terms: 66k + -48k2 + 18k3 = 0 Solving 66k + -48k2 + 18k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6k'. 6k(11 + -8k + 3k2) = 0 Ignore the factor 6.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 '(11 + -8k + 3k2)' equal to zero and attempt to solve: Simplifying 11 + -8k + 3k2 = 0 Solving 11 + -8k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.666666667 + -2.666666667k + k2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + -2.666666667k + -3.666666667 + k2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + -2.666666667k + k2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + -2.666666667k + k2 = 0 + -3.666666667 -2.666666667k + k2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 -2.666666667k + k2 = -3.666666667 The k term is -2.666666667k. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667k + 1.777777780 + k2 = -3.666666667 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667k + k2 = -3.666666667 + 1.777777780 Combine like terms: -3.666666667 + 1.777777780 = -1.888888887 1.777777780 + -2.666666667k + k2 = -1.888888887 Factor a perfect square on the left side: (k + -1.333333334)(k + -1.333333334) = -1.888888887 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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