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Simplifying 6000D2 + -10861.6731029141D + -11581.6949287997 = 0 Reorder the terms: -11581.6949287997 + -10861.6731029141D + 6000D2 = 0 Solving -11581.6949287997 + -10861.6731029141D + 6000D2 = 0 Solving for variable 'D'. Begin completing the square. Divide all terms by 6000 the coefficient of the squared term: Divide each side by '6000'. -1.930282488 + -1.81027885D + D2 = 0 Move the constant term to the right: Add '1.930282488' to each side of the equation. -1.930282488 + -1.81027885D + 1.930282488 + D2 = 0 + 1.930282488 Reorder the terms: -1.930282488 + 1.930282488 + -1.81027885D + D2 = 0 + 1.930282488 Combine like terms: -1.930282488 + 1.930282488 = 0.000000000 0.000000000 + -1.81027885D + D2 = 0 + 1.930282488 -1.81027885D + D2 = 0 + 1.930282488 Combine like terms: 0 + 1.930282488 = 1.930282488 -1.81027885D + D2 = 1.930282488 The D term is -1.81027885D. Take half its coefficient (-0.905139425). Square it (0.8192773787) and add it to both sides. Add '0.8192773787' to each side of the equation. -1.81027885D + 0.8192773787 + D2 = 1.930282488 + 0.8192773787 Reorder the terms: 0.8192773787 + -1.81027885D + D2 = 1.930282488 + 0.8192773787 Combine like terms: 1.930282488 + 0.8192773787 = 2.7495598667 0.8192773787 + -1.81027885D + D2 = 2.7495598667 Factor a perfect square on the left side: (D + -0.905139425)(D + -0.905139425) = 2.7495598667 Calculate the square root of the right side: 1.658179685 Break this problem into two subproblems by setting (D + -0.905139425) equal to 1.658179685 and -1.658179685.Subproblem 1
D + -0.905139425 = 1.658179685 Simplifying D + -0.905139425 = 1.658179685 Reorder the terms: -0.905139425 + D = 1.658179685 Solving -0.905139425 + D = 1.658179685 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '0.905139425' to each side of the equation. -0.905139425 + 0.905139425 + D = 1.658179685 + 0.905139425 Combine like terms: -0.905139425 + 0.905139425 = 0.000000000 0.000000000 + D = 1.658179685 + 0.905139425 D = 1.658179685 + 0.905139425 Combine like terms: 1.658179685 + 0.905139425 = 2.56331911 D = 2.56331911 Simplifying D = 2.56331911Subproblem 2
D + -0.905139425 = -1.658179685 Simplifying D + -0.905139425 = -1.658179685 Reorder the terms: -0.905139425 + D = -1.658179685 Solving -0.905139425 + D = -1.658179685 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '0.905139425' to each side of the equation. -0.905139425 + 0.905139425 + D = -1.658179685 + 0.905139425 Combine like terms: -0.905139425 + 0.905139425 = 0.000000000 0.000000000 + D = -1.658179685 + 0.905139425 D = -1.658179685 + 0.905139425 Combine like terms: -1.658179685 + 0.905139425 = -0.75304026 D = -0.75304026 Simplifying D = -0.75304026Solution
The solution to the problem is based on the solutions from the subproblems. D = {2.56331911, -0.75304026}
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