0=x^4-x^2-42

Solution for 0=x^4-x^2-42 equation:

Simplifying
0 = x4 + -1x2 + -42

Reorder the terms:
0 = -42 + -1x2 + x4

Solving
0 = -42 + -1x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + x2 + -1x4 = -42 + -1x2 + x4 + 42 + x2 + -1x4

Reorder the terms:
42 + x2 + -1x4 = -42 + 42 + -1x2 + x2 + x4 + -1x4

Combine like terms: -42 + 42 = 0
42 + x2 + -1x4 = 0 + -1x2 + x2 + x4 + -1x4
42 + x2 + -1x4 = -1x2 + x2 + x4 + -1x4

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

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

Factor a trinomial.
(7 + -1x2)(6 + x2) = 0

Subproblem 1
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 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 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Subproblem 2
Set the factor '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

Solving
6 + x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x2 = 0 + -6
x2 = 0 + -6

Combine like terms: 0 + -6 = -6
x2 = -6

Simplifying
x2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.645751311, 2.645751311}