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Simplifying x^{4}+ -81 = 0 Reorder the terms: -81 + x^{4}= 0 Solving -81 + x^{4}= 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + x^{4}= 0 + 81 Combine like terms: -81 + 81 = 0 0 + x^{4}= 0 + 81 x^{4}= 0 + 81 Combine like terms: 0 + 81 = 81 x^{4}= 81 Simplifying x^{4}= 81 Reorder the terms: -81 + x^{4}= 81 + -81 Combine like terms: 81 + -81 = 0 -81 + x^{4}= 0 Factor a difference between two squares. (9 + x^{2})(-9 + x^{2}) = 0 Factor a difference between two squares. (9 + x^{2})((3 + x)(-3 + x)) = 0## Subproblem 1

Set the factor '(9 + x^{2})' equal to zero and attempt to solve: Simplifying 9 + x^{2}= 0 Solving 9 + x^{2}= 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x^{2}= 0 + -9 Combine like terms: 9 + -9 = 0 0 + x^{2}= 0 + -9 x^{2}= 0 + -9 Combine like terms: 0 + -9 = -9 x^{2}= -9 Simplifying x^{2}= -9 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3## Subproblem 3

Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3## Solution

x = {-3, 3}

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