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Simplifying d2 + 18d + 81 = 13 Reorder the terms: 81 + 18d + d2 = 13 Solving 81 + 18d + d2 = 13 Solving for variable 'd'. Reorder the terms: 81 + -13 + 18d + d2 = 13 + -13 Combine like terms: 81 + -13 = 68 68 + 18d + d2 = 13 + -13 Combine like terms: 13 + -13 = 0 68 + 18d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + 18d + -68 + d2 = 0 + -68 Reorder the terms: 68 + -68 + 18d + d2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + 18d + d2 = 0 + -68 18d + d2 = 0 + -68 Combine like terms: 0 + -68 = -68 18d + d2 = -68 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 = -68 + 81 Reorder the terms: 81 + 18d + d2 = -68 + 81 Combine like terms: -68 + 81 = 13 81 + 18d + d2 = 13 Factor a perfect square on the left side: (d + 9)(d + 9) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (d + 9) equal to 3.605551275 and -3.605551275.Subproblem 1
d + 9 = 3.605551275 Simplifying d + 9 = 3.605551275 Reorder the terms: 9 + d = 3.605551275 Solving 9 + d = 3.605551275 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 = 3.605551275 + -9 Combine like terms: 9 + -9 = 0 0 + d = 3.605551275 + -9 d = 3.605551275 + -9 Combine like terms: 3.605551275 + -9 = -5.394448725 d = -5.394448725 Simplifying d = -5.394448725Subproblem 2
d + 9 = -3.605551275 Simplifying d + 9 = -3.605551275 Reorder the terms: 9 + d = -3.605551275 Solving 9 + d = -3.605551275 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 = -3.605551275 + -9 Combine like terms: 9 + -9 = 0 0 + d = -3.605551275 + -9 d = -3.605551275 + -9 Combine like terms: -3.605551275 + -9 = -12.605551275 d = -12.605551275 Simplifying d = -12.605551275Solution
The solution to the problem is based on the solutions from the subproblems. d = {-5.394448725, -12.605551275}
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