0=x^4-18x^2-243

Solution for 0=x^4-18x^2-243 equation:

Simplifying
0 = x4 + -18x2 + -243

Reorder the terms:
0 = -243 + -18x2 + x4

Solving
0 = -243 + -18x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 243 = 243
243 + 18x2 + -1x4 = -243 + -18x2 + x4 + 243 + 18x2 + -1x4

Reorder the terms:
243 + 18x2 + -1x4 = -243 + 243 + -18x2 + 18x2 + x4 + -1x4

Combine like terms: -243 + 243 = 0
243 + 18x2 + -1x4 = 0 + -18x2 + 18x2 + x4 + -1x4
243 + 18x2 + -1x4 = -18x2 + 18x2 + x4 + -1x4

Combine like terms: -18x2 + 18x2 = 0
243 + 18x2 + -1x4 = 0 + x4 + -1x4
243 + 18x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
243 + 18x2 + -1x4 = 0

Factor a trinomial.
(27 + -1x2)(9 + x2) = 0

Subproblem 1
Set the factor '(27 + -1x2)' equal to zero and attempt to solve:

Simplifying
27 + -1x2 = 0

Solving
27 + -1x2 = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1x2 = 0 + -27
-1x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-1x2 = -27

Divide each side by '-1'.
x2 = 27

Simplifying
x2 = 27

Take the square root of each side:
x = {-5.196152423, 5.196152423}
Subproblem 2
Set the factor '(9 + x2)' equal to zero and attempt to solve:

Simplifying
9 + x2 = 0

Solving
9 + x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x2 = 0 + -9
x2 = 0 + -9

Combine like terms: 0 + -9 = -9
x2 = -9

Simplifying
x2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-5.196152423, 5.196152423}