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Simplifying 2k(3k + 2) = -20 Reorder the terms: 2k(2 + 3k) = -20 (2 * 2k + 3k * 2k) = -20 (4k + 6k2) = -20 Solving 4k + 6k2 = -20 Solving for variable 'k'. Reorder the terms: 20 + 4k + 6k2 = -20 + 20 Combine like terms: -20 + 20 = 0 20 + 4k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 2k + 3k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 2k + 3k2)' equal to zero and attempt to solve: Simplifying 10 + 2k + 3k2 = 0 Solving 10 + 2k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 0.6666666667k + k2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 0.6666666667k + -3.333333333 + k2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 0.6666666667k + k2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 0.6666666667k + k2 = 0 + -3.333333333 0.6666666667k + k2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 0.6666666667k + k2 = -3.333333333 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 = -3.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667k + k2 = -3.333333333 + 0.1111111112 Combine like terms: -3.333333333 + 0.1111111112 = -3.2222222218 0.1111111112 + 0.6666666667k + k2 = -3.2222222218 Factor a perfect square on the left side: (k + 0.3333333334)(k + 0.3333333334) = -3.2222222218 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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