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Simplifying d2 + -18d + 41 = 0 Reorder the terms: 41 + -18d + d2 = 0 Solving 41 + -18d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -18d + -41 + d2 = 0 + -41 Reorder the terms: 41 + -41 + -18d + d2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -18d + d2 = 0 + -41 -18d + d2 = 0 + -41 Combine like terms: 0 + -41 = -41 -18d + d2 = -41 The d term is -18d. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18d + 81 + d2 = -41 + 81 Reorder the terms: 81 + -18d + d2 = -41 + 81 Combine like terms: -41 + 81 = 40 81 + -18d + d2 = 40 Factor a perfect square on the left side: (d + -9)(d + -9) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (d + -9) equal to 6.32455532 and -6.32455532.Subproblem 1
d + -9 = 6.32455532 Simplifying d + -9 = 6.32455532 Reorder the terms: -9 + d = 6.32455532 Solving -9 + d = 6.32455532 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + d = 6.32455532 + 9 Combine like terms: -9 + 9 = 0 0 + d = 6.32455532 + 9 d = 6.32455532 + 9 Combine like terms: 6.32455532 + 9 = 15.32455532 d = 15.32455532 Simplifying d = 15.32455532Subproblem 2
d + -9 = -6.32455532 Simplifying d + -9 = -6.32455532 Reorder the terms: -9 + d = -6.32455532 Solving -9 + d = -6.32455532 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + d = -6.32455532 + 9 Combine like terms: -9 + 9 = 0 0 + d = -6.32455532 + 9 d = -6.32455532 + 9 Combine like terms: -6.32455532 + 9 = 2.67544468 d = 2.67544468 Simplifying d = 2.67544468Solution
The solution to the problem is based on the solutions from the subproblems. d = {15.32455532, 2.67544468}
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