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Simplifying 0 = x5 + -25x3 + 144x Reorder the terms: 0 = 144x + -25x3 + x5 Solving 0 = 144x + -25x3 + x5 Solving for variable 'x'. Remove the zero: -144x + 25x3 + -1x5 = 144x + -25x3 + x5 + -144x + 25x3 + -1x5 Reorder the terms: -144x + 25x3 + -1x5 = 144x + -144x + -25x3 + 25x3 + x5 + -1x5 Combine like terms: 144x + -144x = 0 -144x + 25x3 + -1x5 = 0 + -25x3 + 25x3 + x5 + -1x5 -144x + 25x3 + -1x5 = -25x3 + 25x3 + x5 + -1x5 Combine like terms: -25x3 + 25x3 = 0 -144x + 25x3 + -1x5 = 0 + x5 + -1x5 -144x + 25x3 + -1x5 = x5 + -1x5 Combine like terms: x5 + -1x5 = 0 -144x + 25x3 + -1x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-144 + 25x2 + -1x4) = 0 Factor a trinomial. x((-16 + x2)(9 + -1x2)) = 0 Factor a difference between two squares. x(((4 + x)(-4 + x))(9 + -1x2)) = 0 Factor a difference between two squares. x(((3 + x)(3 + -1x))(4 + x)(-4 + 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 '(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 3
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 4
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 5
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, -4, 4, -3, 3}
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