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Simplifying d2 + -12d = 20 Reorder the terms: -12d + d2 = 20 Solving -12d + d2 = 20 Solving for variable 'd'. Reorder the terms: -20 + -12d + d2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -12d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -12d + 20 + d2 = 0 + 20 Reorder the terms: -20 + 20 + -12d + d2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -12d + d2 = 0 + 20 -12d + d2 = 0 + 20 Combine like terms: 0 + 20 = 20 -12d + d2 = 20 The d term is -12d. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12d + 36 + d2 = 20 + 36 Reorder the terms: 36 + -12d + d2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + -12d + d2 = 56 Factor a perfect square on the left side: (d + -6)(d + -6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (d + -6) equal to 7.483314774 and -7.483314774.Subproblem 1
d + -6 = 7.483314774 Simplifying d + -6 = 7.483314774 Reorder the terms: -6 + d = 7.483314774 Solving -6 + d = 7.483314774 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = 7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + d = 7.483314774 + 6 d = 7.483314774 + 6 Combine like terms: 7.483314774 + 6 = 13.483314774 d = 13.483314774 Simplifying d = 13.483314774Subproblem 2
d + -6 = -7.483314774 Simplifying d + -6 = -7.483314774 Reorder the terms: -6 + d = -7.483314774 Solving -6 + d = -7.483314774 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + d = -7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + d = -7.483314774 + 6 d = -7.483314774 + 6 Combine like terms: -7.483314774 + 6 = -1.483314774 d = -1.483314774 Simplifying d = -1.483314774Solution
The solution to the problem is based on the solutions from the subproblems. d = {13.483314774, -1.483314774}
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