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Simplifying -9k2 + -8k + -6 = 0 Reorder the terms: -6 + -8k + -9k2 = 0 Solving -6 + -8k + -9k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 8k + 9k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 8k + 9k2)' equal to zero and attempt to solve: Simplifying 6 + 8k + 9k2 = 0 Solving 6 + 8k + 9k2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.6666666667 + 0.8888888889k + k2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 0.8888888889k + -0.6666666667 + k2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 0.8888888889k + k2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 0.8888888889k + k2 = 0 + -0.6666666667 0.8888888889k + k2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 0.8888888889k + k2 = -0.6666666667 The k term is 0.8888888889k. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889k + 0.1975308642 + k2 = -0.6666666667 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889k + k2 = -0.6666666667 + 0.1975308642 Combine like terms: -0.6666666667 + 0.1975308642 = -0.4691358025 0.1975308642 + 0.8888888889k + k2 = -0.4691358025 Factor a perfect square on the left side: (k + 0.4444444445)(k + 0.4444444445) = -0.4691358025 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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