8X^4-31X^2-4=0

Solution for 8X^4-31X^2-4=0 equation:

Simplifying
8X4 + -31X2 + -4 = 0

Reorder the terms:
-4 + -31X2 + 8X4 = 0

Solving
-4 + -31X2 + 8X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(-1 + -8X2)(4 + -1X2) = 0

Factor a difference between two squares.
(-1 + -8X2)((2 + X)(2 + -1X)) = 0

Subproblem 1
Set the factor '(-1 + -8X2)' equal to zero and attempt to solve:

Simplifying
-1 + -8X2 = 0

Solving
-1 + -8X2 = 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 + -8X2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8X2 = 0 + 1
-8X2 = 0 + 1

Combine like terms: 0 + 1 = 1
-8X2 = 1

Divide each side by '-8'.
X2 = -0.125

Simplifying
X2 = -0.125

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 + 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 3
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}