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Simplifying 9050(D2) + -1(0.75 * 565650D) = (315.13) Multiply 0.75 * 565650 9050D2 + -1(424237.5D) = (315.13) Remove parenthesis around (424237.5D) 9050D2 + -1 * 424237.5D = (315.13) Multiply -1 * 424237.5 9050D2 + -424237.5D = (315.13) Reorder the terms: -424237.5D + 9050D2 = (315.13) -424237.5D + 9050D2 = 315.13 Solving -424237.5D + 9050D2 = 315.13 Solving for variable 'D'. Reorder the terms: -315.13 + -424237.5D + 9050D2 = 315.13 + -315.13 Combine like terms: 315.13 + -315.13 = 0.00 -315.13 + -424237.5D + 9050D2 = 0.00 Begin completing the square. Divide all terms by 9050 the coefficient of the squared term: Divide each side by '9050'. -0.03482099448 + -46.87707182D + D2 = 0.00 Move the constant term to the right: Add '0.03482099448' to each side of the equation. -0.03482099448 + -46.87707182D + 0.03482099448 + D2 = 0.00 + 0.03482099448 Reorder the terms: -0.03482099448 + 0.03482099448 + -46.87707182D + D2 = 0.00 + 0.03482099448 Combine like terms: -0.03482099448 + 0.03482099448 = 0.00000000000 0.00000000000 + -46.87707182D + D2 = 0.00 + 0.03482099448 -46.87707182D + D2 = 0.00 + 0.03482099448 Combine like terms: 0.00 + 0.03482099448 = 0.03482099448 -46.87707182D + D2 = 0.03482099448 The D term is -46.87707182D. Take half its coefficient (-23.43853591). Square it (549.3649656) and add it to both sides. Add '549.3649656' to each side of the equation. -46.87707182D + 549.3649656 + D2 = 0.03482099448 + 549.3649656 Reorder the terms: 549.3649656 + -46.87707182D + D2 = 0.03482099448 + 549.3649656 Combine like terms: 0.03482099448 + 549.3649656 = 549.39978659448 549.3649656 + -46.87707182D + D2 = 549.39978659448 Factor a perfect square on the left side: (D + -23.43853591)(D + -23.43853591) = 549.39978659448 Calculate the square root of the right side: 23.439278713 Break this problem into two subproblems by setting (D + -23.43853591) equal to 23.439278713 and -23.439278713.Subproblem 1
D + -23.43853591 = 23.439278713 Simplifying D + -23.43853591 = 23.439278713 Reorder the terms: -23.43853591 + D = 23.439278713 Solving -23.43853591 + D = 23.439278713 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '23.43853591' to each side of the equation. -23.43853591 + 23.43853591 + D = 23.439278713 + 23.43853591 Combine like terms: -23.43853591 + 23.43853591 = 0.00000000 0.00000000 + D = 23.439278713 + 23.43853591 D = 23.439278713 + 23.43853591 Combine like terms: 23.439278713 + 23.43853591 = 46.877814623 D = 46.877814623 Simplifying D = 46.877814623Subproblem 2
D + -23.43853591 = -23.439278713 Simplifying D + -23.43853591 = -23.439278713 Reorder the terms: -23.43853591 + D = -23.439278713 Solving -23.43853591 + D = -23.439278713 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '23.43853591' to each side of the equation. -23.43853591 + 23.43853591 + D = -23.439278713 + 23.43853591 Combine like terms: -23.43853591 + 23.43853591 = 0.00000000 0.00000000 + D = -23.439278713 + 23.43853591 D = -23.439278713 + 23.43853591 Combine like terms: -23.439278713 + 23.43853591 = -0.000742803 D = -0.000742803 Simplifying D = -0.000742803Solution
The solution to the problem is based on the solutions from the subproblems. D = {46.877814623, -0.000742803}
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