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Simplifying x5 = 3x3 + 54x Reorder the terms: x5 = 54x + 3x3 Solving x5 = 54x + 3x3 Solving for variable 'x'. Reorder the terms: -54x + -3x3 + x5 = 54x + 3x3 + -54x + -3x3 Reorder the terms: -54x + -3x3 + x5 = 54x + -54x + 3x3 + -3x3 Combine like terms: 54x + -54x = 0 -54x + -3x3 + x5 = 0 + 3x3 + -3x3 -54x + -3x3 + x5 = 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -54x + -3x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-54 + -3x2 + x4) = 0 Factor a trinomial. x((-6 + -1x2)(9 + -1x2)) = 0 Factor a difference between two squares. x((-6 + -1x2)((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 '(-6 + -1x2)' equal to zero and attempt to solve: Simplifying -6 + -1x2 = 0 Solving -6 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x2 = 0 + 6 -1x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1x2 = 6 Divide each side by '-1'. x2 = -6 Simplifying x2 = -6 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 '(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 4
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}
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