0=x^4-x^2-56

Solution for 0=x^4-x^2-56 equation:

Simplifying
0 = x4 + -1x2 + -56

Reorder the terms:
0 = -56 + -1x2 + x4

Solving
0 = -56 + -1x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 56 = 56
56 + x2 + -1x4 = -56 + -1x2 + x4 + 56 + x2 + -1x4

Reorder the terms:
56 + x2 + -1x4 = -56 + 56 + -1x2 + x2 + x4 + -1x4

Combine like terms: -56 + 56 = 0
56 + x2 + -1x4 = 0 + -1x2 + x2 + x4 + -1x4
56 + x2 + -1x4 = -1x2 + x2 + x4 + -1x4

Combine like terms: -1x2 + x2 = 0
56 + x2 + -1x4 = 0 + x4 + -1x4
56 + x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
56 + x2 + -1x4 = 0

Factor a trinomial.
(8 + -1x2)(7 + x2) = 0

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

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 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 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Subproblem 2
Set the factor '(7 + x2)' equal to zero and attempt to solve:

Simplifying
7 + x2 = 0

Solving
7 + x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x2 = 0 + -7
x2 = 0 + -7

Combine like terms: 0 + -7 = -7
x2 = -7

Simplifying
x2 = -7

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.828427125, 2.828427125}