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Simplifying d4 + -18d2 + 81 = 0 Reorder the terms: 81 + -18d2 + d4 = 0 Solving 81 + -18d2 + d4 = 0 Solving for variable 'd'. Factor a trinomial. (9 + -1d2)(9 + -1d2) = 0 Factor a difference between two squares. ((3 + d)(3 + -1d))(9 + -1d2) = 0 Factor a difference between two squares. ((3 + d)(3 + -1d))(3 + d)(3 + -1d) = 0Subproblem 1
Set the factor '(3 + d)' equal to zero and attempt to solve: Simplifying 3 + d = 0 Solving 3 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + d = 0 + -3 d = 0 + -3 Combine like terms: 0 + -3 = -3 d = -3 Simplifying d = -3Subproblem 2
Set the factor '(3 + -1d)' equal to zero and attempt to solve: Simplifying 3 + -1d = 0 Solving 3 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1d = 0 + -3 -1d = 0 + -3 Combine like terms: 0 + -3 = -3 -1d = -3 Divide each side by '-1'. d = 3 Simplifying d = 3Subproblem 3
Set the factor '(3 + d)' equal to zero and attempt to solve: Simplifying 3 + d = 0 Solving 3 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + d = 0 + -3 d = 0 + -3 Combine like terms: 0 + -3 = -3 d = -3 Simplifying d = -3Subproblem 4
Set the factor '(3 + -1d)' equal to zero and attempt to solve: Simplifying 3 + -1d = 0 Solving 3 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1d = 0 + -3 -1d = 0 + -3 Combine like terms: 0 + -3 = -3 -1d = -3 Divide each side by '-1'. d = 3 Simplifying d = 3Solution
d = {-3, 3, -3, 3}
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