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Simplifying 76.2d2 + 5806d = 35600 Reorder the terms: 5806d + 76.2d2 = 35600 Solving 5806d + 76.2d2 = 35600 Solving for variable 'd'. Reorder the terms: -35600 + 5806d + 76.2d2 = 35600 + -35600 Combine like terms: 35600 + -35600 = 0 -35600 + 5806d + 76.2d2 = 0 Begin completing the square. Divide all terms by 76.2 the coefficient of the squared term: Divide each side by '76.2'. -467.191601 + 76.19422572d + d2 = 0 Move the constant term to the right: Add '467.191601' to each side of the equation. -467.191601 + 76.19422572d + 467.191601 + d2 = 0 + 467.191601 Reorder the terms: -467.191601 + 467.191601 + 76.19422572d + d2 = 0 + 467.191601 Combine like terms: -467.191601 + 467.191601 = 0.000000 0.000000 + 76.19422572d + d2 = 0 + 467.191601 76.19422572d + d2 = 0 + 467.191601 Combine like terms: 0 + 467.191601 = 467.191601 76.19422572d + d2 = 467.191601 The d term is 76.19422572d. Take half its coefficient (38.09711286). Square it (1451.390008) and add it to both sides. Add '1451.390008' to each side of the equation. 76.19422572d + 1451.390008 + d2 = 467.191601 + 1451.390008 Reorder the terms: 1451.390008 + 76.19422572d + d2 = 467.191601 + 1451.390008 Combine like terms: 467.191601 + 1451.390008 = 1918.581609 1451.390008 + 76.19422572d + d2 = 1918.581609 Factor a perfect square on the left side: (d + 38.09711286)(d + 38.09711286) = 1918.581609 Calculate the square root of the right side: 43.801616511 Break this problem into two subproblems by setting (d + 38.09711286) equal to 43.801616511 and -43.801616511.Subproblem 1
d + 38.09711286 = 43.801616511 Simplifying d + 38.09711286 = 43.801616511 Reorder the terms: 38.09711286 + d = 43.801616511 Solving 38.09711286 + d = 43.801616511 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-38.09711286' to each side of the equation. 38.09711286 + -38.09711286 + d = 43.801616511 + -38.09711286 Combine like terms: 38.09711286 + -38.09711286 = 0.00000000 0.00000000 + d = 43.801616511 + -38.09711286 d = 43.801616511 + -38.09711286 Combine like terms: 43.801616511 + -38.09711286 = 5.704503651 d = 5.704503651 Simplifying d = 5.704503651Subproblem 2
d + 38.09711286 = -43.801616511 Simplifying d + 38.09711286 = -43.801616511 Reorder the terms: 38.09711286 + d = -43.801616511 Solving 38.09711286 + d = -43.801616511 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-38.09711286' to each side of the equation. 38.09711286 + -38.09711286 + d = -43.801616511 + -38.09711286 Combine like terms: 38.09711286 + -38.09711286 = 0.00000000 0.00000000 + d = -43.801616511 + -38.09711286 d = -43.801616511 + -38.09711286 Combine like terms: -43.801616511 + -38.09711286 = -81.898729371 d = -81.898729371 Simplifying d = -81.898729371Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.704503651, -81.898729371}
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