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Simplifying d2 = 50 + -53d Solving d2 = 50 + -53d Solving for variable 'd'. Reorder the terms: -50 + 53d + d2 = 50 + -53d + -50 + 53d Reorder the terms: -50 + 53d + d2 = 50 + -50 + -53d + 53d Combine like terms: 50 + -50 = 0 -50 + 53d + d2 = 0 + -53d + 53d -50 + 53d + d2 = -53d + 53d Combine like terms: -53d + 53d = 0 -50 + 53d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 53d + 50 + d2 = 0 + 50 Reorder the terms: -50 + 50 + 53d + d2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 53d + d2 = 0 + 50 53d + d2 = 0 + 50 Combine like terms: 0 + 50 = 50 53d + d2 = 50 The d term is 53d. Take half its coefficient (26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. 53d + 702.25 + d2 = 50 + 702.25 Reorder the terms: 702.25 + 53d + d2 = 50 + 702.25 Combine like terms: 50 + 702.25 = 752.25 702.25 + 53d + d2 = 752.25 Factor a perfect square on the left side: (d + 26.5)(d + 26.5) = 752.25 Calculate the square root of the right side: 27.427176304 Break this problem into two subproblems by setting (d + 26.5) equal to 27.427176304 and -27.427176304.Subproblem 1
d + 26.5 = 27.427176304 Simplifying d + 26.5 = 27.427176304 Reorder the terms: 26.5 + d = 27.427176304 Solving 26.5 + d = 27.427176304 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + d = 27.427176304 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + d = 27.427176304 + -26.5 d = 27.427176304 + -26.5 Combine like terms: 27.427176304 + -26.5 = 0.927176304 d = 0.927176304 Simplifying d = 0.927176304Subproblem 2
d + 26.5 = -27.427176304 Simplifying d + 26.5 = -27.427176304 Reorder the terms: 26.5 + d = -27.427176304 Solving 26.5 + d = -27.427176304 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + d = -27.427176304 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + d = -27.427176304 + -26.5 d = -27.427176304 + -26.5 Combine like terms: -27.427176304 + -26.5 = -53.927176304 d = -53.927176304 Simplifying d = -53.927176304Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.927176304, -53.927176304}
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