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Simplifying d2 + 403.34d + -284.625 = 0 Reorder the terms: -284.625 + 403.34d + d2 = 0 Solving -284.625 + 403.34d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '284.625' to each side of the equation. -284.625 + 403.34d + 284.625 + d2 = 0 + 284.625 Reorder the terms: -284.625 + 284.625 + 403.34d + d2 = 0 + 284.625 Combine like terms: -284.625 + 284.625 = 0.000 0.000 + 403.34d + d2 = 0 + 284.625 403.34d + d2 = 0 + 284.625 Combine like terms: 0 + 284.625 = 284.625 403.34d + d2 = 284.625 The d term is 403.34d. Take half its coefficient (201.67). Square it (40670.7889) and add it to both sides. Add '40670.7889' to each side of the equation. 403.34d + 40670.7889 + d2 = 284.625 + 40670.7889 Reorder the terms: 40670.7889 + 403.34d + d2 = 284.625 + 40670.7889 Combine like terms: 284.625 + 40670.7889 = 40955.4139 40670.7889 + 403.34d + d2 = 40955.4139 Factor a perfect square on the left side: (d + 201.67)(d + 201.67) = 40955.4139 Calculate the square root of the right side: 202.374439839 Break this problem into two subproblems by setting (d + 201.67) equal to 202.374439839 and -202.374439839.Subproblem 1
d + 201.67 = 202.374439839 Simplifying d + 201.67 = 202.374439839 Reorder the terms: 201.67 + d = 202.374439839 Solving 201.67 + d = 202.374439839 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-201.67' to each side of the equation. 201.67 + -201.67 + d = 202.374439839 + -201.67 Combine like terms: 201.67 + -201.67 = 0.00 0.00 + d = 202.374439839 + -201.67 d = 202.374439839 + -201.67 Combine like terms: 202.374439839 + -201.67 = 0.704439839 d = 0.704439839 Simplifying d = 0.704439839Subproblem 2
d + 201.67 = -202.374439839 Simplifying d + 201.67 = -202.374439839 Reorder the terms: 201.67 + d = -202.374439839 Solving 201.67 + d = -202.374439839 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-201.67' to each side of the equation. 201.67 + -201.67 + d = -202.374439839 + -201.67 Combine like terms: 201.67 + -201.67 = 0.00 0.00 + d = -202.374439839 + -201.67 d = -202.374439839 + -201.67 Combine like terms: -202.374439839 + -201.67 = -404.044439839 d = -404.044439839 Simplifying d = -404.044439839Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.704439839, -404.044439839}
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