2*x^8-4*x^4=16

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Solution for 2*x^8-4*x^4=16 equation: 


Simplifying
2x8 + -4x4 = 16

Reorder the terms:
-4x4 + 2x8 = 16

Solving
-4x4 + 2x8 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -4x4 + 2x8 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -4x4 + 2x8 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x4 + x8) = 0

Factor a trinomial.
2((-2 + -1x4)(4 + -1x4)) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -1x4)' equal to zero and attempt to solve:

Simplifying
-2 + -1x4 = 0

Solving
-2 + -1x4 = 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 + -1x4 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x4 = 0 + 2
-1x4 = 0 + 2

Combine like terms: 0 + 2 = 2
-1x4 = 2

Divide each side by '-1'.
x4 = -2

Simplifying
x4 = -2

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 '(2 + x2)' equal to zero and attempt to solve:

Simplifying
2 + x2 = 0

Solving
2 + x2 = 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 + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 0 + -2
x2 = 0 + -2

Combine like terms: 0 + -2 = -2
x2 = -2

Simplifying
x2 = -2

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 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {-1.414213562, 1.414213562}

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