2x^8-7x^4-4=0

Solution for 2x^8-7x^4-4=0 equation:

Simplifying
2x8 + -7x4 + -4 = 0

Reorder the terms:
-4 + -7x4 + 2x8 = 0

Solving
-4 + -7x4 + 2x8 = 0

Solving for variable 'x'.

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

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

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

Simplifying
-1 + -2x4 = 0

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

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

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

Divide each side by '-2'.
x4 = -0.5

Simplifying
x4 = -0.5

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}