x^8-24x^4+128=0

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Solution for x^8-24x^4+128=0 equation:


Simplifying
x8 + -24x4 + 128 = 0

Reorder the terms:
128 + -24x4 + x8 = 0

Solving
128 + -24x4 + x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -1x4)(16 + -1x4) = 0

Factor a difference between two squares.
(8 + -1x4)((4 + x2)(4 + -1x2)) = 0

Factor a difference between two squares.
(8 + -1x4)((4 + x2)((2 + x)(2 + -1x))) = 0

Subproblem 1

Set the factor '(8 + -1x4)' equal to zero and attempt to solve: Simplifying 8 + -1x4 = 0 Solving 8 + -1x4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x4 = 0 + -8 -1x4 = 0 + -8 Combine like terms: 0 + -8 = -8 -1x4 = -8 Divide each side by '-1'. x4 = 8 Simplifying x4 = 8 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 '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 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 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 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 '(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 = -2

Subproblem 4

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-2, 2}

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