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Simplifying d2 + -4d + -31 = 0 Reorder the terms: -31 + -4d + d2 = 0 Solving -31 + -4d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -4d + 31 + d2 = 0 + 31 Reorder the terms: -31 + 31 + -4d + d2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -4d + d2 = 0 + 31 -4d + d2 = 0 + 31 Combine like terms: 0 + 31 = 31 -4d + d2 = 31 The d term is -4d. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4d + 4 + d2 = 31 + 4 Reorder the terms: 4 + -4d + d2 = 31 + 4 Combine like terms: 31 + 4 = 35 4 + -4d + d2 = 35 Factor a perfect square on the left side: (d + -2)(d + -2) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (d + -2) equal to 5.916079783 and -5.916079783.Subproblem 1
d + -2 = 5.916079783 Simplifying d + -2 = 5.916079783 Reorder the terms: -2 + d = 5.916079783 Solving -2 + d = 5.916079783 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 5.916079783 + 2 Combine like terms: -2 + 2 = 0 0 + d = 5.916079783 + 2 d = 5.916079783 + 2 Combine like terms: 5.916079783 + 2 = 7.916079783 d = 7.916079783 Simplifying d = 7.916079783Subproblem 2
d + -2 = -5.916079783 Simplifying d + -2 = -5.916079783 Reorder the terms: -2 + d = -5.916079783 Solving -2 + d = -5.916079783 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = -5.916079783 + 2 Combine like terms: -2 + 2 = 0 0 + d = -5.916079783 + 2 d = -5.916079783 + 2 Combine like terms: -5.916079783 + 2 = -3.916079783 d = -3.916079783 Simplifying d = -3.916079783Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.916079783, -3.916079783}
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