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Simplifying -3k(2k + -2) = 12 Reorder the terms: -3k(-2 + 2k) = 12 (-2 * -3k + 2k * -3k) = 12 (6k + -6k2) = 12 Solving 6k + -6k2 = 12 Solving for variable 'k'. Reorder the terms: -12 + 6k + -6k2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 6k + -6k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + k + -1k2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + k + -1k2)' equal to zero and attempt to solve: Simplifying -2 + k + -1k2 = 0 Solving -2 + k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -1k + k2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1k + -2 + k2 = 0 + -2 Reorder the terms: 2 + -2 + -1k + k2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1k + k2 = 0 + -2 -1k + k2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1k + k2 = -2 The k term is k. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1k + 0.25 + k2 = -2 + 0.25 Reorder the terms: 0.25 + -1k + k2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -1k + k2 = -1.75 Factor a perfect square on the left side: (k + 0.5)(k + 0.5) = -1.75 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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