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Simplifying (2272.38D * D) + -2(6048.75) * D + -24718.69 = 0 Multiply D * D (2272.38D2) + -2(6048.75) * D + -24718.69 = 0 Multiply -2 * 6048.75 (2272.38D2) + -12097.5D + -24718.69 = 0 Reorder the terms: -24718.69 + -12097.5D + (2272.38D2) = 0 Solving -24718.69 + -12097.5D + (2272.38D2) = 0 Solving for variable 'D'. Begin completing the square. Divide all terms by 2272.38 the coefficient of the squared term: Divide each side by '2272.38'. -10.87788574 + -5.323713463D + D2 = 0 Move the constant term to the right: Add '10.87788574' to each side of the equation. -10.87788574 + -5.323713463D + 10.87788574 + D2 = 0 + 10.87788574 Reorder the terms: -10.87788574 + 10.87788574 + -5.323713463D + D2 = 0 + 10.87788574 Combine like terms: -10.87788574 + 10.87788574 = 0.00000000 0.00000000 + -5.323713463D + D2 = 0 + 10.87788574 -5.323713463D + D2 = 0 + 10.87788574 Combine like terms: 0 + 10.87788574 = 10.87788574 -5.323713463D + D2 = 10.87788574 The D term is -5.323713463D. Take half its coefficient (-2.661856732). Square it (7.085481262) and add it to both sides. Add '7.085481262' to each side of the equation. -5.323713463D + 7.085481262 + D2 = 10.87788574 + 7.085481262 Reorder the terms: 7.085481262 + -5.323713463D + D2 = 10.87788574 + 7.085481262 Combine like terms: 10.87788574 + 7.085481262 = 17.963367002 7.085481262 + -5.323713463D + D2 = 17.963367002 Factor a perfect square on the left side: ((D) + -2.661856732)((D) + -2.661856732) = 17.963367002 Calculate the square root of the right side: 4.238321248 Break this problem into two subproblems by setting ((D) + -2.661856732) equal to 4.238321248 and -4.238321248.Subproblem 1
(D) + -2.661856732 = 4.238321248 Simplifying (D) + -2.661856732 = 4.238321248 D + -2.661856732 = 4.238321248 Reorder the terms: -2.661856732 + D = 4.238321248 Solving -2.661856732 + D = 4.238321248 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '2.661856732' to each side of the equation. -2.661856732 + 2.661856732 + D = 4.238321248 + 2.661856732 Combine like terms: -2.661856732 + 2.661856732 = 0.000000000 0.000000000 + D = 4.238321248 + 2.661856732 D = 4.238321248 + 2.661856732 Combine like terms: 4.238321248 + 2.661856732 = 6.90017798 D = 6.90017798 Simplifying D = 6.90017798Subproblem 2
(D) + -2.661856732 = -4.238321248 Simplifying (D) + -2.661856732 = -4.238321248 D + -2.661856732 = -4.238321248 Reorder the terms: -2.661856732 + D = -4.238321248 Solving -2.661856732 + D = -4.238321248 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '2.661856732' to each side of the equation. -2.661856732 + 2.661856732 + D = -4.238321248 + 2.661856732 Combine like terms: -2.661856732 + 2.661856732 = 0.000000000 0.000000000 + D = -4.238321248 + 2.661856732 D = -4.238321248 + 2.661856732 Combine like terms: -4.238321248 + 2.661856732 = -1.576464516 D = -1.576464516 Simplifying D = -1.576464516Solution
The solution to the problem is based on the solutions from the subproblems. D = {6.90017798, -1.576464516}
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