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Simplifying 12k2 + 22k + 60 = 0 Reorder the terms: 60 + 22k + 12k2 = 0 Solving 60 + 22k + 12k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + 11k + 6k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + 11k + 6k2)' equal to zero and attempt to solve: Simplifying 30 + 11k + 6k2 = 0 Solving 30 + 11k + 6k2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 5 + 1.833333333k + k2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 1.833333333k + -5 + k2 = 0 + -5 Reorder the terms: 5 + -5 + 1.833333333k + k2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 1.833333333k + k2 = 0 + -5 1.833333333k + k2 = 0 + -5 Combine like terms: 0 + -5 = -5 1.833333333k + k2 = -5 The k term is 1.833333333k. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333k + 0.8402777775 + k2 = -5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333k + k2 = -5 + 0.8402777775 Combine like terms: -5 + 0.8402777775 = -4.1597222225 0.8402777775 + 1.833333333k + k2 = -4.1597222225 Factor a perfect square on the left side: (k + 0.9166666665)(k + 0.9166666665) = -4.1597222225 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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