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Simplifying x5 = 18x3 + -81x Reorder the terms: x5 = -81x + 18x3 Solving x5 = -81x + 18x3 Solving for variable 'x'. Reorder the terms: 81x + -18x3 + x5 = -81x + 18x3 + 81x + -18x3 Reorder the terms: 81x + -18x3 + x5 = -81x + 81x + 18x3 + -18x3 Combine like terms: -81x + 81x = 0 81x + -18x3 + x5 = 0 + 18x3 + -18x3 81x + -18x3 + x5 = 18x3 + -18x3 Combine like terms: 18x3 + -18x3 = 0 81x + -18x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(81 + -18x2 + x4) = 0 Factor a trinomial. x((9 + -1x2)(9 + -1x2)) = 0 Factor a difference between two squares. x(((3 + x)(3 + -1x))(9 + -1x2)) = 0 Factor a difference between two squares. x(((3 + x)(3 + -1x))(3 + x)(3 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = -3Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 4
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 = -3Subproblem 5
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, -3, 3, -3, 3}
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