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Simplifying 0 = x5 + 4x3 + -5x Reorder the terms: 0 = -5x + 4x3 + x5 Solving 0 = -5x + 4x3 + x5 Solving for variable 'x'. Remove the zero: 5x + -4x3 + -1x5 = -5x + 4x3 + x5 + 5x + -4x3 + -1x5 Reorder the terms: 5x + -4x3 + -1x5 = -5x + 5x + 4x3 + -4x3 + x5 + -1x5 Combine like terms: -5x + 5x = 0 5x + -4x3 + -1x5 = 0 + 4x3 + -4x3 + x5 + -1x5 5x + -4x3 + -1x5 = 4x3 + -4x3 + x5 + -1x5 Combine like terms: 4x3 + -4x3 = 0 5x + -4x3 + -1x5 = 0 + x5 + -1x5 5x + -4x3 + -1x5 = x5 + -1x5 Combine like terms: x5 + -1x5 = 0 5x + -4x3 + -1x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -4x2 + -1x4) = 0 Factor a trinomial. x((1 + -1x2)(5 + x2)) = 0 Factor a difference between two squares. x(((1 + x)(1 + -1x))(5 + x2)) = 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 '(5 + x2)' equal to zero and attempt to solve: Simplifying 5 + x2 = 0 Solving 5 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 0 + -5 x2 = 0 + -5 Combine like terms: 0 + -5 = -5 x2 = -5 Simplifying x2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, -1, 1}
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