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Simplifying d4 + 6d2 + 2 = 0 Reorder the terms: 2 + 6d2 + d4 = 0 Solving 2 + 6d2 + d4 = 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 + 6d2 + -2 + d4 = 0 + -2 Reorder the terms: 2 + -2 + 6d2 + d4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6d2 + d4 = 0 + -2 6d2 + d4 = 0 + -2 Combine like terms: 0 + -2 = -2 6d2 + d4 = -2 The d term is 6d2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6d2 + 9 + d4 = -2 + 9 Reorder the terms: 9 + 6d2 + d4 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6d2 + d4 = 7 Factor a perfect square on the left side: (d2 + 3)(d2 + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (d2 + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
d2 + 3 = 2.645751311 Simplifying d2 + 3 = 2.645751311 Reorder the terms: 3 + d2 = 2.645751311 Solving 3 + d2 = 2.645751311 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d2 = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + d2 = 2.645751311 + -3 d2 = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 d2 = -0.354248689 Simplifying d2 = -0.354248689 Reorder the terms: 0.354248689 + d2 = -0.354248689 + 0.354248689 Combine like terms: -0.354248689 + 0.354248689 = 0.000000000 0.354248689 + d2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
d2 + 3 = -2.645751311 Simplifying d2 + 3 = -2.645751311 Reorder the terms: 3 + d2 = -2.645751311 Solving 3 + d2 = -2.645751311 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d2 = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + d2 = -2.645751311 + -3 d2 = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 d2 = -5.645751311 Simplifying d2 = -5.645751311 Reorder the terms: 5.645751311 + d2 = -5.645751311 + 5.645751311 Combine like terms: -5.645751311 + 5.645751311 = 0.000000000 5.645751311 + d2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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