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Simplifying 12.99D + 14.24D2 = 12.825 Solving 12.99D + 14.24D2 = 12.825 Solving for variable 'D'. Reorder the terms: -12.825 + 12.99D + 14.24D2 = 12.825 + -12.825 Combine like terms: 12.825 + -12.825 = 0.000 -12.825 + 12.99D + 14.24D2 = 0.000 Begin completing the square. Divide all terms by 14.24 the coefficient of the squared term: Divide each side by '14.24'. -0.9006320225 + 0.9122191011D + D2 = 0.0 Move the constant term to the right: Add '0.9006320225' to each side of the equation. -0.9006320225 + 0.9122191011D + 0.9006320225 + D2 = 0.0 + 0.9006320225 Reorder the terms: -0.9006320225 + 0.9006320225 + 0.9122191011D + D2 = 0.0 + 0.9006320225 Combine like terms: -0.9006320225 + 0.9006320225 = 0.0000000000 0.0000000000 + 0.9122191011D + D2 = 0.0 + 0.9006320225 0.9122191011D + D2 = 0.0 + 0.9006320225 Combine like terms: 0.0 + 0.9006320225 = 0.9006320225 0.9122191011D + D2 = 0.9006320225 The D term is 0.9122191011D. Take half its coefficient (0.4561095506). Square it (0.2080359221) and add it to both sides. Add '0.2080359221' to each side of the equation. 0.9122191011D + 0.2080359221 + D2 = 0.9006320225 + 0.2080359221 Reorder the terms: 0.2080359221 + 0.9122191011D + D2 = 0.9006320225 + 0.2080359221 Combine like terms: 0.9006320225 + 0.2080359221 = 1.1086679446 0.2080359221 + 0.9122191011D + D2 = 1.1086679446 Factor a perfect square on the left side: (D + 0.4561095506)(D + 0.4561095506) = 1.1086679446 Calculate the square root of the right side: 1.05293302 Break this problem into two subproblems by setting (D + 0.4561095506) equal to 1.05293302 and -1.05293302.Subproblem 1
D + 0.4561095506 = 1.05293302 Simplifying D + 0.4561095506 = 1.05293302 Reorder the terms: 0.4561095506 + D = 1.05293302 Solving 0.4561095506 + D = 1.05293302 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '-0.4561095506' to each side of the equation. 0.4561095506 + -0.4561095506 + D = 1.05293302 + -0.4561095506 Combine like terms: 0.4561095506 + -0.4561095506 = 0.0000000000 0.0000000000 + D = 1.05293302 + -0.4561095506 D = 1.05293302 + -0.4561095506 Combine like terms: 1.05293302 + -0.4561095506 = 0.5968234694 D = 0.5968234694 Simplifying D = 0.5968234694Subproblem 2
D + 0.4561095506 = -1.05293302 Simplifying D + 0.4561095506 = -1.05293302 Reorder the terms: 0.4561095506 + D = -1.05293302 Solving 0.4561095506 + D = -1.05293302 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '-0.4561095506' to each side of the equation. 0.4561095506 + -0.4561095506 + D = -1.05293302 + -0.4561095506 Combine like terms: 0.4561095506 + -0.4561095506 = 0.0000000000 0.0000000000 + D = -1.05293302 + -0.4561095506 D = -1.05293302 + -0.4561095506 Combine like terms: -1.05293302 + -0.4561095506 = -1.5090425706 D = -1.5090425706 Simplifying D = -1.5090425706Solution
The solution to the problem is based on the solutions from the subproblems. D = {0.5968234694, -1.5090425706}
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