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Simplifying 1100d + -1d2 = 58416.95 Solving 1100d + -1d2 = 58416.95 Solving for variable 'd'. Reorder the terms: -58416.95 + 1100d + -1d2 = 58416.95 + -58416.95 Combine like terms: 58416.95 + -58416.95 = 0.00 -58416.95 + 1100d + -1d2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 58416.95 + -1100d + d2 = 0.00 Move the constant term to the right: Add '-58416.95' to each side of the equation. 58416.95 + -1100d + -58416.95 + d2 = 0.00 + -58416.95 Reorder the terms: 58416.95 + -58416.95 + -1100d + d2 = 0.00 + -58416.95 Combine like terms: 58416.95 + -58416.95 = 0.00 0.00 + -1100d + d2 = 0.00 + -58416.95 -1100d + d2 = 0.00 + -58416.95 Combine like terms: 0.00 + -58416.95 = -58416.95 -1100d + d2 = -58416.95 The d term is -1100d. Take half its coefficient (-550). Square it (302500) and add it to both sides. Add '302500' to each side of the equation. -1100d + 302500 + d2 = -58416.95 + 302500 Reorder the terms: 302500 + -1100d + d2 = -58416.95 + 302500 Combine like terms: -58416.95 + 302500 = 244083.05 302500 + -1100d + d2 = 244083.05 Factor a perfect square on the left side: (d + -550)(d + -550) = 244083.05 Calculate the square root of the right side: 494.047619162 Break this problem into two subproblems by setting (d + -550) equal to 494.047619162 and -494.047619162.Subproblem 1
d + -550 = 494.047619162 Simplifying d + -550 = 494.047619162 Reorder the terms: -550 + d = 494.047619162 Solving -550 + d = 494.047619162 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + d = 494.047619162 + 550 Combine like terms: -550 + 550 = 0 0 + d = 494.047619162 + 550 d = 494.047619162 + 550 Combine like terms: 494.047619162 + 550 = 1044.047619162 d = 1044.047619162 Simplifying d = 1044.047619162Subproblem 2
d + -550 = -494.047619162 Simplifying d + -550 = -494.047619162 Reorder the terms: -550 + d = -494.047619162 Solving -550 + d = -494.047619162 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '550' to each side of the equation. -550 + 550 + d = -494.047619162 + 550 Combine like terms: -550 + 550 = 0 0 + d = -494.047619162 + 550 d = -494.047619162 + 550 Combine like terms: -494.047619162 + 550 = 55.952380838 d = 55.952380838 Simplifying d = 55.952380838Solution
The solution to the problem is based on the solutions from the subproblems. d = {1044.047619162, 55.952380838}
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