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Simplifying d2 + -14d = 41 Reorder the terms: -14d + d2 = 41 Solving -14d + d2 = 41 Solving for variable 'd'. Reorder the terms: -41 + -14d + d2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -14d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -14d + 41 + d2 = 0 + 41 Reorder the terms: -41 + 41 + -14d + d2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -14d + d2 = 0 + 41 -14d + d2 = 0 + 41 Combine like terms: 0 + 41 = 41 -14d + d2 = 41 The d term is -14d. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14d + 49 + d2 = 41 + 49 Reorder the terms: 49 + -14d + d2 = 41 + 49 Combine like terms: 41 + 49 = 90 49 + -14d + d2 = 90 Factor a perfect square on the left side: (d + -7)(d + -7) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (d + -7) equal to 9.486832981 and -9.486832981.Subproblem 1
d + -7 = 9.486832981 Simplifying d + -7 = 9.486832981 Reorder the terms: -7 + d = 9.486832981 Solving -7 + d = 9.486832981 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + d = 9.486832981 + 7 Combine like terms: -7 + 7 = 0 0 + d = 9.486832981 + 7 d = 9.486832981 + 7 Combine like terms: 9.486832981 + 7 = 16.486832981 d = 16.486832981 Simplifying d = 16.486832981Subproblem 2
d + -7 = -9.486832981 Simplifying d + -7 = -9.486832981 Reorder the terms: -7 + d = -9.486832981 Solving -7 + d = -9.486832981 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + d = -9.486832981 + 7 Combine like terms: -7 + 7 = 0 0 + d = -9.486832981 + 7 d = -9.486832981 + 7 Combine like terms: -9.486832981 + 7 = -2.486832981 d = -2.486832981 Simplifying d = -2.486832981Solution
The solution to the problem is based on the solutions from the subproblems. d = {16.486832981, -2.486832981}
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