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Simplifying 1100d + -1d2 = 31692.94 Solving 1100d + -1d2 = 31692.94 Solving for variable 'd'. Reorder the terms: -31692.94 + 1100d + -1d2 = 31692.94 + -31692.94 Combine like terms: 31692.94 + -31692.94 = 0.00 -31692.94 + 1100d + -1d2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 31692.94 + -1100d + d2 = 0.00 Move the constant term to the right: Add '-31692.94' to each side of the equation. 31692.94 + -1100d + -31692.94 + d2 = 0.00 + -31692.94 Reorder the terms: 31692.94 + -31692.94 + -1100d + d2 = 0.00 + -31692.94 Combine like terms: 31692.94 + -31692.94 = 0.00 0.00 + -1100d + d2 = 0.00 + -31692.94 -1100d + d2 = 0.00 + -31692.94 Combine like terms: 0.00 + -31692.94 = -31692.94 -1100d + d2 = -31692.94 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 = -31692.94 + 302500 Reorder the terms: 302500 + -1100d + d2 = -31692.94 + 302500 Combine like terms: -31692.94 + 302500 = 270807.06 302500 + -1100d + d2 = 270807.06 Factor a perfect square on the left side: (d + -550)(d + -550) = 270807.06 Calculate the square root of the right side: 520.391256652 Break this problem into two subproblems by setting (d + -550) equal to 520.391256652 and -520.391256652.Subproblem 1
d + -550 = 520.391256652 Simplifying d + -550 = 520.391256652 Reorder the terms: -550 + d = 520.391256652 Solving -550 + d = 520.391256652 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 = 520.391256652 + 550 Combine like terms: -550 + 550 = 0 0 + d = 520.391256652 + 550 d = 520.391256652 + 550 Combine like terms: 520.391256652 + 550 = 1070.391256652 d = 1070.391256652 Simplifying d = 1070.391256652Subproblem 2
d + -550 = -520.391256652 Simplifying d + -550 = -520.391256652 Reorder the terms: -550 + d = -520.391256652 Solving -550 + d = -520.391256652 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 = -520.391256652 + 550 Combine like terms: -550 + 550 = 0 0 + d = -520.391256652 + 550 d = -520.391256652 + 550 Combine like terms: -520.391256652 + 550 = 29.608743348 d = 29.608743348 Simplifying d = 29.608743348Solution
The solution to the problem is based on the solutions from the subproblems. d = {1070.391256652, 29.608743348}
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