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Simplifying 3d2 + -84d + 27 = 0 Reorder the terms: 27 + -84d + 3d2 = 0 Solving 27 + -84d + 3d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -28d + d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -28d + d2)' equal to zero and attempt to solve: Simplifying 9 + -28d + d2 = 0 Solving 9 + -28d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -28d + -9 + d2 = 0 + -9 Reorder the terms: 9 + -9 + -28d + d2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -28d + d2 = 0 + -9 -28d + d2 = 0 + -9 Combine like terms: 0 + -9 = -9 -28d + d2 = -9 The d term is -28d. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28d + 196 + d2 = -9 + 196 Reorder the terms: 196 + -28d + d2 = -9 + 196 Combine like terms: -9 + 196 = 187 196 + -28d + d2 = 187 Factor a perfect square on the left side: (d + -14)(d + -14) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (d + -14) equal to 13.674794331 and -13.674794331.Subproblem 1
d + -14 = 13.674794331 Simplifying d + -14 = 13.674794331 Reorder the terms: -14 + d = 13.674794331 Solving -14 + d = 13.674794331 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + d = 13.674794331 + 14 Combine like terms: -14 + 14 = 0 0 + d = 13.674794331 + 14 d = 13.674794331 + 14 Combine like terms: 13.674794331 + 14 = 27.674794331 d = 27.674794331 Simplifying d = 27.674794331Subproblem 2
d + -14 = -13.674794331 Simplifying d + -14 = -13.674794331 Reorder the terms: -14 + d = -13.674794331 Solving -14 + d = -13.674794331 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + d = -13.674794331 + 14 Combine like terms: -14 + 14 = 0 0 + d = -13.674794331 + 14 d = -13.674794331 + 14 Combine like terms: -13.674794331 + 14 = 0.325205669 d = 0.325205669 Simplifying d = 0.325205669Solution
The solution to the problem is based on the solutions from the subproblems. d = {27.674794331, 0.325205669}Solution
d = {27.674794331, 0.325205669}
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