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Simplifying 18 + 14k + 6k2 = 0 Solving 18 + 14k + 6k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 7k + 3k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 7k + 3k2)' equal to zero and attempt to solve: Simplifying 9 + 7k + 3k2 = 0 Solving 9 + 7k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 2.333333333k + k2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2.333333333k + -3 + k2 = 0 + -3 Reorder the terms: 3 + -3 + 2.333333333k + k2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2.333333333k + k2 = 0 + -3 2.333333333k + k2 = 0 + -3 Combine like terms: 0 + -3 = -3 2.333333333k + k2 = -3 The k term is 2.333333333k. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333k + 1.361111112 + k2 = -3 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333k + k2 = -3 + 1.361111112 Combine like terms: -3 + 1.361111112 = -1.638888888 1.361111112 + 2.333333333k + k2 = -1.638888888 Factor a perfect square on the left side: (k + 1.166666667)(k + 1.166666667) = -1.638888888 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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