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Simplifying x13 + 15x9 + -16x5 = 0 Reorder the terms: -16x5 + 15x9 + x13 = 0 Solving -16x5 + 15x9 + x13 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x5'. x5(-16 + 15x4 + x8) = 0 Factor a trinomial. x5((-16 + -1x4)(1 + -1x4)) = 0 Factor a difference between two squares. x5((-16 + -1x4)((1 + x2)(1 + -1x2))) = 0 Factor a difference between two squares. x5((-16 + -1x4)((1 + x2)((1 + x)(1 + -1x)))) = 0Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 0 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 '(-16 + -1x4)' equal to zero and attempt to solve: Simplifying -16 + -1x4 = 0 Solving -16 + -1x4 = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x4 = 0 + 16 -1x4 = 0 + 16 Combine like terms: 0 + 16 = 16 -1x4 = 16 Divide each side by '-1'. x4 = -16 Simplifying x4 = -16 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 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 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 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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 = {-1, 1}
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