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Simplifying 6k2 + -4k + 72 = 0 Reorder the terms: 72 + -4k + 6k2 = 0 Solving 72 + -4k + 6k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -2k + 3k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + -2k + 3k2)' equal to zero and attempt to solve: Simplifying 36 + -2k + 3k2 = 0 Solving 36 + -2k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 12 + -0.6666666667k + k2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -0.6666666667k + -12 + k2 = 0 + -12 Reorder the terms: 12 + -12 + -0.6666666667k + k2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -0.6666666667k + k2 = 0 + -12 -0.6666666667k + k2 = 0 + -12 Combine like terms: 0 + -12 = -12 -0.6666666667k + k2 = -12 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 = -12 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667k + k2 = -12 + 0.1111111112 Combine like terms: -12 + 0.1111111112 = -11.8888888888 0.1111111112 + -0.6666666667k + k2 = -11.8888888888 Factor a perfect square on the left side: (k + -0.3333333334)(k + -0.3333333334) = -11.8888888888 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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