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Simplifying 16d8 + -8d4 + 1 = 0 Reorder the terms: 1 + -8d4 + 16d8 = 0 Solving 1 + -8d4 + 16d8 = 0 Solving for variable 'd'. Factor a trinomial. (1 + -4d4)(1 + -4d4) = 0 Factor a difference between two squares. ((1 + 2d2)(1 + -2d2))(1 + -4d4) = 0 Factor a difference between two squares. ((1 + 2d2)(1 + -2d2))(1 + 2d2)(1 + -2d2) = 0Subproblem 1
Set the factor '(1 + 2d2)' equal to zero and attempt to solve: Simplifying 1 + 2d2 = 0 Solving 1 + 2d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2d2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2d2 = 0 + -1 2d2 = 0 + -1 Combine like terms: 0 + -1 = -1 2d2 = -1 Divide each side by '2'. d2 = -0.5 Simplifying d2 = -0.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -2d2)' equal to zero and attempt to solve: Simplifying 1 + -2d2 = 0 Solving 1 + -2d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2d2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2d2 = 0 + -1 -2d2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2d2 = -1 Divide each side by '-2'. d2 = 0.5 Simplifying d2 = 0.5 Take the square root of each side: d = {-0.707106781, 0.707106781}Subproblem 3
Set the factor '(1 + 2d2)' equal to zero and attempt to solve: Simplifying 1 + 2d2 = 0 Solving 1 + 2d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2d2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2d2 = 0 + -1 2d2 = 0 + -1 Combine like terms: 0 + -1 = -1 2d2 = -1 Divide each side by '2'. d2 = -0.5 Simplifying d2 = -0.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(1 + -2d2)' equal to zero and attempt to solve: Simplifying 1 + -2d2 = 0 Solving 1 + -2d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2d2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2d2 = 0 + -1 -2d2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2d2 = -1 Divide each side by '-2'. d2 = 0.5 Simplifying d2 = 0.5 Take the square root of each side: d = {-0.707106781, 0.707106781}Solution
d = {-0.707106781, 0.707106781, -0.707106781, 0.707106781}
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