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Simplifying 0 = -1x5 + 17x3 + -16x Reorder the terms: 0 = -16x + 17x3 + -1x5 Solving 0 = -16x + 17x3 + -1x5 Solving for variable 'x'. Remove the zero: 16x + -17x3 + x5 = -16x + 17x3 + -1x5 + 16x + -17x3 + x5 Reorder the terms: 16x + -17x3 + x5 = -16x + 16x + 17x3 + -17x3 + -1x5 + x5 Combine like terms: -16x + 16x = 0 16x + -17x3 + x5 = 0 + 17x3 + -17x3 + -1x5 + x5 16x + -17x3 + x5 = 17x3 + -17x3 + -1x5 + x5 Combine like terms: 17x3 + -17x3 = 0 16x + -17x3 + x5 = 0 + -1x5 + x5 16x + -17x3 + x5 = -1x5 + x5 Combine like terms: -1x5 + x5 = 0 16x + -17x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(16 + -17x2 + x4) = 0 Factor a trinomial. x((1 + -1x2)(16 + -1x2)) = 0 Factor a difference between two squares. x(((1 + x)(1 + -1x))(16 + -1x2)) = 0 Factor a difference between two squares. x(((4 + x)(4 + -1x))(1 + x)(1 + -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 '(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 3
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 = 1Subproblem 4
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 5
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, -1, 1, -4, 4}
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