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Simplifying 0 = 4x4 + 27x2 + -81 Reorder the terms: 0 = -81 + 27x2 + 4x4 Solving 0 = -81 + 27x2 + 4x4 Solving for variable 'x'. Combine like terms: 0 + 81 = 81 81 + -27x2 + -4x4 = -81 + 27x2 + 4x4 + 81 + -27x2 + -4x4 Reorder the terms: 81 + -27x2 + -4x4 = -81 + 81 + 27x2 + -27x2 + 4x4 + -4x4 Combine like terms: -81 + 81 = 0 81 + -27x2 + -4x4 = 0 + 27x2 + -27x2 + 4x4 + -4x4 81 + -27x2 + -4x4 = 27x2 + -27x2 + 4x4 + -4x4 Combine like terms: 27x2 + -27x2 = 0 81 + -27x2 + -4x4 = 0 + 4x4 + -4x4 81 + -27x2 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 81 + -27x2 + -4x4 = 0 Factor a trinomial. (9 + -4x2)(9 + x2) = 0 Factor a difference between two squares. ((3 + 2x)(3 + -2x))(9 + x2) = 0Subproblem 1
Set the factor '(9 + x2)' equal to zero and attempt to solve: Simplifying 9 + x2 = 0 Solving 9 + x2 = 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 + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x2 = 0 + -9 x2 = 0 + -9 Combine like terms: 0 + -9 = -9 x2 = -9 Simplifying x2 = -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 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1.5, 1.5}
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