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Simplifying 6k2 + 36k + 432 = 0 Reorder the terms: 432 + 36k + 6k2 = 0 Solving 432 + 36k + 6k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6'. 6(72 + 6k + k2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(72 + 6k + k2)' equal to zero and attempt to solve: Simplifying 72 + 6k + k2 = 0 Solving 72 + 6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + 6k + -72 + k2 = 0 + -72 Reorder the terms: 72 + -72 + 6k + k2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + 6k + k2 = 0 + -72 6k + k2 = 0 + -72 Combine like terms: 0 + -72 = -72 6k + k2 = -72 The k term is 6k. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6k + 9 + k2 = -72 + 9 Reorder the terms: 9 + 6k + k2 = -72 + 9 Combine like terms: -72 + 9 = -63 9 + 6k + k2 = -63 Factor a perfect square on the left side: (k + 3)(k + 3) = -63 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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