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Simplifying 10k2 + -12k + 72 = 0 Reorder the terms: 72 + -12k + 10k2 = 0 Solving 72 + -12k + 10k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -6k + 5k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + -6k + 5k2)' equal to zero and attempt to solve: Simplifying 36 + -6k + 5k2 = 0 Solving 36 + -6k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -1.2k + k2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -1.2k + -7.2 + k2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -1.2k + k2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -1.2k + k2 = 0 + -7.2 -1.2k + k2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -1.2k + k2 = -7.2 The k term is -1.2k. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2k + 0.36 + k2 = -7.2 + 0.36 Reorder the terms: 0.36 + -1.2k + k2 = -7.2 + 0.36 Combine like terms: -7.2 + 0.36 = -6.84 0.36 + -1.2k + k2 = -6.84 Factor a perfect square on the left side: (k + -0.6)(k + -0.6) = -6.84 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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