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Simplifying 35000 = 2297.3D2 + 18378.3D Reorder the terms: 35000 = 18378.3D + 2297.3D2 Solving 35000 = 18378.3D + 2297.3D2 Solving for variable 'D'. Reorder the terms: 35000 + -18378.3D + -2297.3D2 = 18378.3D + -18378.3D + 2297.3D2 + -2297.3D2 Combine like terms: 18378.3D + -18378.3D = 0.0 35000 + -18378.3D + -2297.3D2 = 0.0 + 2297.3D2 + -2297.3D2 35000 + -18378.3D + -2297.3D2 = 2297.3D2 + -2297.3D2 Combine like terms: 2297.3D2 + -2297.3D2 = 0.0 35000 + -18378.3D + -2297.3D2 = 0.0 Begin completing the square. Divide all terms by -2297.3 the coefficient of the squared term: Divide each side by '-2297.3'. -15.23527619 + 7.999956471D + D2 = 0 Move the constant term to the right: Add '15.23527619' to each side of the equation. -15.23527619 + 7.999956471D + 15.23527619 + D2 = 0 + 15.23527619 Reorder the terms: -15.23527619 + 15.23527619 + 7.999956471D + D2 = 0 + 15.23527619 Combine like terms: -15.23527619 + 15.23527619 = 0.00000000 0.00000000 + 7.999956471D + D2 = 0 + 15.23527619 7.999956471D + D2 = 0 + 15.23527619 Combine like terms: 0 + 15.23527619 = 15.23527619 7.999956471D + D2 = 15.23527619 The D term is 7.999956471D. Take half its coefficient (3.999978236). Square it (15.99982589) and add it to both sides. Add '15.99982589' to each side of the equation. 7.999956471D + 15.99982589 + D2 = 15.23527619 + 15.99982589 Reorder the terms: 15.99982589 + 7.999956471D + D2 = 15.23527619 + 15.99982589 Combine like terms: 15.23527619 + 15.99982589 = 31.23510208 15.99982589 + 7.999956471D + D2 = 31.23510208 Factor a perfect square on the left side: (D + 3.999978236)(D + 3.999978236) = 31.23510208 Calculate the square root of the right side: 5.588837274 Break this problem into two subproblems by setting (D + 3.999978236) equal to 5.588837274 and -5.588837274.Subproblem 1
D + 3.999978236 = 5.588837274 Simplifying D + 3.999978236 = 5.588837274 Reorder the terms: 3.999978236 + D = 5.588837274 Solving 3.999978236 + D = 5.588837274 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '-3.999978236' to each side of the equation. 3.999978236 + -3.999978236 + D = 5.588837274 + -3.999978236 Combine like terms: 3.999978236 + -3.999978236 = 0.000000000 0.000000000 + D = 5.588837274 + -3.999978236 D = 5.588837274 + -3.999978236 Combine like terms: 5.588837274 + -3.999978236 = 1.588859038 D = 1.588859038 Simplifying D = 1.588859038Subproblem 2
D + 3.999978236 = -5.588837274 Simplifying D + 3.999978236 = -5.588837274 Reorder the terms: 3.999978236 + D = -5.588837274 Solving 3.999978236 + D = -5.588837274 Solving for variable 'D'. Move all terms containing D to the left, all other terms to the right. Add '-3.999978236' to each side of the equation. 3.999978236 + -3.999978236 + D = -5.588837274 + -3.999978236 Combine like terms: 3.999978236 + -3.999978236 = 0.000000000 0.000000000 + D = -5.588837274 + -3.999978236 D = -5.588837274 + -3.999978236 Combine like terms: -5.588837274 + -3.999978236 = -9.58881551 D = -9.58881551 Simplifying D = -9.58881551Solution
The solution to the problem is based on the solutions from the subproblems. D = {1.588859038, -9.58881551}
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