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Simplifying d2 + 2d + -2 = 0 Reorder the terms: -2 + 2d + d2 = 0 Solving -2 + 2d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 2d + 2 + d2 = 0 + 2 Reorder the terms: -2 + 2 + 2d + d2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2d + d2 = 0 + 2 2d + d2 = 0 + 2 Combine like terms: 0 + 2 = 2 2d + d2 = 2 The d term is 2d. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2d + 1 + d2 = 2 + 1 Reorder the terms: 1 + 2d + d2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2d + d2 = 3 Factor a perfect square on the left side: (d + 1)(d + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (d + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
d + 1 = 1.732050808 Simplifying d + 1 = 1.732050808 Reorder the terms: 1 + d = 1.732050808 Solving 1 + d = 1.732050808 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + d = 1.732050808 + -1 d = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 d = 0.732050808 Simplifying d = 0.732050808Subproblem 2
d + 1 = -1.732050808 Simplifying d + 1 = -1.732050808 Reorder the terms: 1 + d = -1.732050808 Solving 1 + d = -1.732050808 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + d = -1.732050808 + -1 d = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 d = -2.732050808 Simplifying d = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.732050808, -2.732050808}
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