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Simplifying 0 = -1d2 + 12d + 6 Reorder the terms: 0 = 6 + 12d + -1d2 Solving 0 = 6 + 12d + -1d2 Solving for variable 'd'. Combine like terms: 0 + -6 = -6 -6 + -12d + d2 = 6 + 12d + -1d2 + -6 + -12d + d2 Reorder the terms: -6 + -12d + d2 = 6 + -6 + 12d + -12d + -1d2 + d2 Combine like terms: 6 + -6 = 0 -6 + -12d + d2 = 0 + 12d + -12d + -1d2 + d2 -6 + -12d + d2 = 12d + -12d + -1d2 + d2 Combine like terms: 12d + -12d = 0 -6 + -12d + d2 = 0 + -1d2 + d2 -6 + -12d + d2 = -1d2 + d2 Combine like terms: -1d2 + d2 = 0 -6 + -12d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -12d + 6 + d2 = 0 + 6 Reorder the terms: -6 + 6 + -12d + d2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -12d + d2 = 0 + 6 -12d + d2 = 0 + 6 Combine like terms: 0 + 6 = 6 -12d + d2 = 6 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 = 6 + 36 Reorder the terms: 36 + -12d + d2 = 6 + 36 Combine like terms: 6 + 36 = 42 36 + -12d + d2 = 42 Factor a perfect square on the left side: (d + -6)(d + -6) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (d + -6) equal to 6.480740698 and -6.480740698.Subproblem 1
d + -6 = 6.480740698 Simplifying d + -6 = 6.480740698 Reorder the terms: -6 + d = 6.480740698 Solving -6 + d = 6.480740698 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 = 6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + d = 6.480740698 + 6 d = 6.480740698 + 6 Combine like terms: 6.480740698 + 6 = 12.480740698 d = 12.480740698 Simplifying d = 12.480740698Subproblem 2
d + -6 = -6.480740698 Simplifying d + -6 = -6.480740698 Reorder the terms: -6 + d = -6.480740698 Solving -6 + d = -6.480740698 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 = -6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + d = -6.480740698 + 6 d = -6.480740698 + 6 Combine like terms: -6.480740698 + 6 = -0.480740698 d = -0.480740698 Simplifying d = -0.480740698Solution
The solution to the problem is based on the solutions from the subproblems. d = {12.480740698, -0.480740698}
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