x^8-8x^4+7=0

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Solution for x^8-8x^4+7=0 equation:


Simplifying
x8 + -8x4 + 7 = 0

Reorder the terms:
7 + -8x4 + x8 = 0

Solving
7 + -8x4 + x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x4)(7 + -1x4) = 0

Factor a difference between two squares.
((1 + x2)(1 + -1x2))(7 + -1x4) = 0

Factor a difference between two squares.
((1 + x2)((1 + x)(1 + -1x)))(7 + -1x4) = 0

Subproblem 1

Set the factor '(7 + -1x4)' equal to zero and attempt to solve: Simplifying 7 + -1x4 = 0 Solving 7 + -1x4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x4 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x4 = 0 + -7 -1x4 = 0 + -7 Combine like terms: 0 + -7 = -7 -1x4 = -7 Divide each side by '-1'. x4 = 7 Simplifying x4 = 7 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 '(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 3

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 = -1

Subproblem 4

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 = 1

Solution

x = {-1, 1}

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