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Simplifying -12k[k + 4] = 60 Reorder the terms: -12k[4 + k] = 60 [4 * -12k + k * -12k] = 60 [-48k + -12k2] = 60 Solving -48k + -12k2 = 60 Solving for variable 'k'. Reorder the terms: -60 + -48k + -12k2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -48k + -12k2 = 0 Factor out the Greatest Common Factor (GCF), '-12'. -12(5 + 4k + k2) = 0 Ignore the factor -12.Subproblem 1
Set the factor '(5 + 4k + k2)' equal to zero and attempt to solve: Simplifying 5 + 4k + k2 = 0 Solving 5 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4k + -5 + k2 = 0 + -5 Reorder the terms: 5 + -5 + 4k + k2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4k + k2 = 0 + -5 4k + k2 = 0 + -5 Combine like terms: 0 + -5 = -5 4k + k2 = -5 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = -5 + 4 Reorder the terms: 4 + 4k + k2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4k + k2 = -1 Factor a perfect square on the left side: (k + 2)(k + 2) = -1 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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