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Simplifying k(-6 + -5k) + 4(k + -3) = 0 (-6 * k + -5k * k) + 4(k + -3) = 0 (-6k + -5k2) + 4(k + -3) = 0 Reorder the terms: -6k + -5k2 + 4(-3 + k) = 0 -6k + -5k2 + (-3 * 4 + k * 4) = 0 -6k + -5k2 + (-12 + 4k) = 0 Reorder the terms: -12 + -6k + 4k + -5k2 = 0 Combine like terms: -6k + 4k = -2k -12 + -2k + -5k2 = 0 Solving -12 + -2k + -5k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 2k + 5k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 2k + 5k2)' equal to zero and attempt to solve: Simplifying 12 + 2k + 5k2 = 0 Solving 12 + 2k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 0.4k + k2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 0.4k + -2.4 + k2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 0.4k + k2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 0.4k + k2 = 0 + -2.4 0.4k + k2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 0.4k + k2 = -2.4 The k term is 0.4k. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4k + 0.04 + k2 = -2.4 + 0.04 Reorder the terms: 0.04 + 0.4k + k2 = -2.4 + 0.04 Combine like terms: -2.4 + 0.04 = -2.36 0.04 + 0.4k + k2 = -2.36 Factor a perfect square on the left side: (k + 0.2)(k + 0.2) = -2.36 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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