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Simplifying -18 + -6k = 6k(1 + 3k) -18 + -6k = (1 * 6k + 3k * 6k) -18 + -6k = (6k + 18k2) Solving -18 + -6k = 6k + 18k2 Solving for variable 'k'. Combine like terms: -6k + -6k = -12k -18 + -12k + -18k2 = 6k + 18k2 + -6k + -18k2 Reorder the terms: -18 + -12k + -18k2 = 6k + -6k + 18k2 + -18k2 Combine like terms: 6k + -6k = 0 -18 + -12k + -18k2 = 0 + 18k2 + -18k2 -18 + -12k + -18k2 = 18k2 + -18k2 Combine like terms: 18k2 + -18k2 = 0 -18 + -12k + -18k2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(3 + 2k + 3k2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(3 + 2k + 3k2)' equal to zero and attempt to solve: Simplifying 3 + 2k + 3k2 = 0 Solving 3 + 2k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 0.6666666667k + k2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.6666666667k + -1 + k2 = 0 + -1 Reorder the terms: 1 + -1 + 0.6666666667k + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.6666666667k + k2 = 0 + -1 0.6666666667k + k2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.6666666667k + k2 = -1 The k term is 0.6666666667k. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667k + 0.1111111112 + k2 = -1 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667k + k2 = -1 + 0.1111111112 Combine like terms: -1 + 0.1111111112 = -0.8888888888 0.1111111112 + 0.6666666667k + k2 = -0.8888888888 Factor a perfect square on the left side: (k + 0.3333333334)(k + 0.3333333334) = -0.8888888888 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. The solution to this equation could not be determined.
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