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Simplifying d2 + 100d + -6250 = 0 Reorder the terms: -6250 + 100d + d2 = 0 Solving -6250 + 100d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '6250' to each side of the equation. -6250 + 100d + 6250 + d2 = 0 + 6250 Reorder the terms: -6250 + 6250 + 100d + d2 = 0 + 6250 Combine like terms: -6250 + 6250 = 0 0 + 100d + d2 = 0 + 6250 100d + d2 = 0 + 6250 Combine like terms: 0 + 6250 = 6250 100d + d2 = 6250 The d term is 100d. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100d + 2500 + d2 = 6250 + 2500 Reorder the terms: 2500 + 100d + d2 = 6250 + 2500 Combine like terms: 6250 + 2500 = 8750 2500 + 100d + d2 = 8750 Factor a perfect square on the left side: (d + 50)(d + 50) = 8750 Calculate the square root of the right side: 93.541434669 Break this problem into two subproblems by setting (d + 50) equal to 93.541434669 and -93.541434669.Subproblem 1
d + 50 = 93.541434669 Simplifying d + 50 = 93.541434669 Reorder the terms: 50 + d = 93.541434669 Solving 50 + d = 93.541434669 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + d = 93.541434669 + -50 Combine like terms: 50 + -50 = 0 0 + d = 93.541434669 + -50 d = 93.541434669 + -50 Combine like terms: 93.541434669 + -50 = 43.541434669 d = 43.541434669 Simplifying d = 43.541434669Subproblem 2
d + 50 = -93.541434669 Simplifying d + 50 = -93.541434669 Reorder the terms: 50 + d = -93.541434669 Solving 50 + d = -93.541434669 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + d = -93.541434669 + -50 Combine like terms: 50 + -50 = 0 0 + d = -93.541434669 + -50 d = -93.541434669 + -50 Combine like terms: -93.541434669 + -50 = -143.541434669 d = -143.541434669 Simplifying d = -143.541434669Solution
The solution to the problem is based on the solutions from the subproblems. d = {43.541434669, -143.541434669}
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