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Simplifying d2 + 8d + 1 = 0 Reorder the terms: 1 + 8d + d2 = 0 Solving 1 + 8d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 8d + -1 + d2 = 0 + -1 Reorder the terms: 1 + -1 + 8d + d2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8d + d2 = 0 + -1 8d + d2 = 0 + -1 Combine like terms: 0 + -1 = -1 8d + d2 = -1 The d term is 8d. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8d + 16 + d2 = -1 + 16 Reorder the terms: 16 + 8d + d2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + 8d + d2 = 15 Factor a perfect square on the left side: (d + 4)(d + 4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (d + 4) equal to 3.872983346 and -3.872983346.Subproblem 1
d + 4 = 3.872983346 Simplifying d + 4 = 3.872983346 Reorder the terms: 4 + d = 3.872983346 Solving 4 + d = 3.872983346 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = 3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + d = 3.872983346 + -4 d = 3.872983346 + -4 Combine like terms: 3.872983346 + -4 = -0.127016654 d = -0.127016654 Simplifying d = -0.127016654Subproblem 2
d + 4 = -3.872983346 Simplifying d + 4 = -3.872983346 Reorder the terms: 4 + d = -3.872983346 Solving 4 + d = -3.872983346 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = -3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + d = -3.872983346 + -4 d = -3.872983346 + -4 Combine like terms: -3.872983346 + -4 = -7.872983346 d = -7.872983346 Simplifying d = -7.872983346Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.127016654, -7.872983346}
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