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Simplifying 0 = x5 + -5x3 + 4x Reorder the terms: 0 = 4x + -5x3 + x5 Solving 0 = 4x + -5x3 + x5 Solving for variable 'x'. Remove the zero: -4x + 5x3 + -1x5 = 4x + -5x3 + x5 + -4x + 5x3 + -1x5 Reorder the terms: -4x + 5x3 + -1x5 = 4x + -4x + -5x3 + 5x3 + x5 + -1x5 Combine like terms: 4x + -4x = 0 -4x + 5x3 + -1x5 = 0 + -5x3 + 5x3 + x5 + -1x5 -4x + 5x3 + -1x5 = -5x3 + 5x3 + x5 + -1x5 Combine like terms: -5x3 + 5x3 = 0 -4x + 5x3 + -1x5 = 0 + x5 + -1x5 -4x + 5x3 + -1x5 = x5 + -1x5 Combine like terms: x5 + -1x5 = 0 -4x + 5x3 + -1x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 5x2 + -1x4) = 0 Factor a trinomial. x((-4 + x2)(1 + -1x2)) = 0 Factor a difference between two squares. x(((2 + x)(-2 + x))(1 + -1x2)) = 0 Factor a difference between two squares. x(((1 + x)(1 + -1x))(2 + x)(-2 + x)) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 4
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 5
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, -2, 2, -1, 1}
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