31-4x^2=x^4-1

Solution for 31-4x^2=x^4-1 equation:

Simplifying
31 + -4x2 = x4 + -1

Reorder the terms:
31 + -4x2 = -1 + x4

Solving
31 + -4x2 = -1 + x4

Solving for variable 'x'.

Reorder the terms:
31 + 1 + -4x2 + -1x4 = -1 + x4 + 1 + -1x4

Combine like terms: 31 + 1 = 32
32 + -4x2 + -1x4 = -1 + x4 + 1 + -1x4

Reorder the terms:
32 + -4x2 + -1x4 = -1 + 1 + x4 + -1x4

Combine like terms: -1 + 1 = 0
32 + -4x2 + -1x4 = 0 + x4 + -1x4
32 + -4x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
32 + -4x2 + -1x4 = 0

Factor a trinomial.
(4 + -1x2)(8 + x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(8 + x2) = 0

Subproblem 1
Set the factor '(8 + x2)' equal to zero and attempt to solve:

Simplifying
8 + x2 = 0

Solving
8 + x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x2 = 0 + -8
x2 = 0 + -8

Combine like terms: 0 + -8 = -8
x2 = -8

Simplifying
x2 = -8

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}