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Simplifying 3218.41(D2) + -13433.42D + -6048.65 = 0 Reorder the terms: -6048.65 + -13433.42D + 3218.41D2 = 0 Solving -6048.65 + -13433.42D + 3218.41D2 = 0 Solving for variable 'D'. Begin completing the square. Divide all terms by 3218.41 the coefficient of the squared term: Divide each side by '3218.41'. -1.879390755 + -4.173930605D + D2 = 0 Move the constant term to the right: Add '1.879390755' to each side of the equation. -1.879390755 + -4.173930605D + 1.879390755 + D2 = 0 + 1.879390755 Reorder the terms: -1.879390755 + 1.879390755 + -4.173930605D + D2 = 0 + 1.879390755 Combine like terms: -1.879390755 + 1.879390755 = 0.000000000 0.000000000 + -4.173930605D + D2 = 0 + 1.879390755 -4.173930605D + D2 = 0 + 1.879390755 Combine like terms: 0 + 1.879390755 = 1.879390755 -4.173930605D + D2 = 1.879390755 The D term is -4.173930605D. Take half its coefficient (-2.086965303). Square it (4.355424176) and add it to both sides. Add '4.355424176' to each side of the equation. -4.173930605D + 4.355424176 + D2 = 1.879390755 + 4.355424176 Reorder the terms: 4.355424176 + -4.173930605D + D2 = 1.879390755 + 4.355424176 Combine like terms: 1.879390755 + 4.355424176 = 6.234814931 4.355424176 + -4.173930605D + D2 = 6.234814931 Factor a perfect square on the left side: (D + -2.086965303)(D + -2.086965303) = 6.234814931 Calculate the square root of the right side: 2.496961139 Break this problem into two subproblems by setting (D + -2.086965303) equal to 2.496961139 and -2.496961139.Subproblem 1
D + -2.086965303 = 2.496961139 Simplifying D + -2.086965303 = 2.496961139 Reorder the terms: -2.086965303 + D = 2.496961139 Solving -2.086965303 + D = 2.496961139 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '2.086965303' to each side of the equation. -2.086965303 + 2.086965303 + D = 2.496961139 + 2.086965303 Combine like terms: -2.086965303 + 2.086965303 = 0.000000000 0.000000000 + D = 2.496961139 + 2.086965303 D = 2.496961139 + 2.086965303 Combine like terms: 2.496961139 + 2.086965303 = 4.583926442 D = 4.583926442 Simplifying D = 4.583926442Subproblem 2
D + -2.086965303 = -2.496961139 Simplifying D + -2.086965303 = -2.496961139 Reorder the terms: -2.086965303 + D = -2.496961139 Solving -2.086965303 + D = -2.496961139 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '2.086965303' to each side of the equation. -2.086965303 + 2.086965303 + D = -2.496961139 + 2.086965303 Combine like terms: -2.086965303 + 2.086965303 = 0.000000000 0.000000000 + D = -2.496961139 + 2.086965303 D = -2.496961139 + 2.086965303 Combine like terms: -2.496961139 + 2.086965303 = -0.409995836 D = -0.409995836 Simplifying D = -0.409995836Solution
The solution to the problem is based on the solutions from the subproblems. D = {4.583926442, -0.409995836}
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