x^8+3x^4=4

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Solution for x^8+3x^4=4 equation:


Simplifying
x8 + 3x4 = 4

Reorder the terms:
3x4 + x8 = 4

Solving
3x4 + x8 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 3x4 + x8 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 3x4 + x8 = 0

Factor a trinomial.
(-4 + -1x4)(1 + -1x4) = 0

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

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

Subproblem 1

Set the factor '(-4 + -1x4)' equal to zero and attempt to solve: Simplifying -4 + -1x4 = 0 Solving -4 + -1x4 = 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 + -1x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x4 = 0 + 4 -1x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x4 = 4 Divide each side by '-1'. x4 = -4 Simplifying x4 = -4 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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