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Simplifying 88.9d2 + 7903d = 35600 Reorder the terms: 7903d + 88.9d2 = 35600 Solving 7903d + 88.9d2 = 35600 Solving for variable 'd'. Reorder the terms: -35600 + 7903d + 88.9d2 = 35600 + -35600 Combine like terms: 35600 + -35600 = 0 -35600 + 7903d + 88.9d2 = 0 Begin completing the square. Divide all terms by 88.9 the coefficient of the squared term: Divide each side by '88.9'. -400.4499438 + 88.8976378d + d2 = 0 Move the constant term to the right: Add '400.4499438' to each side of the equation. -400.4499438 + 88.8976378d + 400.4499438 + d2 = 0 + 400.4499438 Reorder the terms: -400.4499438 + 400.4499438 + 88.8976378d + d2 = 0 + 400.4499438 Combine like terms: -400.4499438 + 400.4499438 = 0.0000000 0.0000000 + 88.8976378d + d2 = 0 + 400.4499438 88.8976378d + d2 = 0 + 400.4499438 Combine like terms: 0 + 400.4499438 = 400.4499438 88.8976378d + d2 = 400.4499438 The d term is 88.8976378d. Take half its coefficient (44.4488189). Square it (1975.697502) and add it to both sides. Add '1975.697502' to each side of the equation. 88.8976378d + 1975.697502 + d2 = 400.4499438 + 1975.697502 Reorder the terms: 1975.697502 + 88.8976378d + d2 = 400.4499438 + 1975.697502 Combine like terms: 400.4499438 + 1975.697502 = 2376.1474458 1975.697502 + 88.8976378d + d2 = 2376.1474458 Factor a perfect square on the left side: (d + 44.4488189)(d + 44.4488189) = 2376.1474458 Calculate the square root of the right side: 48.745742848 Break this problem into two subproblems by setting (d + 44.4488189) equal to 48.745742848 and -48.745742848.Subproblem 1
d + 44.4488189 = 48.745742848 Simplifying d + 44.4488189 = 48.745742848 Reorder the terms: 44.4488189 + d = 48.745742848 Solving 44.4488189 + d = 48.745742848 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-44.4488189' to each side of the equation. 44.4488189 + -44.4488189 + d = 48.745742848 + -44.4488189 Combine like terms: 44.4488189 + -44.4488189 = 0.0000000 0.0000000 + d = 48.745742848 + -44.4488189 d = 48.745742848 + -44.4488189 Combine like terms: 48.745742848 + -44.4488189 = 4.296923948 d = 4.296923948 Simplifying d = 4.296923948Subproblem 2
d + 44.4488189 = -48.745742848 Simplifying d + 44.4488189 = -48.745742848 Reorder the terms: 44.4488189 + d = -48.745742848 Solving 44.4488189 + d = -48.745742848 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-44.4488189' to each side of the equation. 44.4488189 + -44.4488189 + d = -48.745742848 + -44.4488189 Combine like terms: 44.4488189 + -44.4488189 = 0.0000000 0.0000000 + d = -48.745742848 + -44.4488189 d = -48.745742848 + -44.4488189 Combine like terms: -48.745742848 + -44.4488189 = -93.194561748 d = -93.194561748 Simplifying d = -93.194561748Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.296923948, -93.194561748}
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