2X^4-9X^2-18=0

Solution for 2X^4-9X^2-18=0 equation:

Simplifying
2X4 + -9X2 + -18 = 0

Reorder the terms:
-18 + -9X2 + 2X4 = 0

Solving
-18 + -9X2 + 2X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(-3 + -2X2)(6 + -1X2) = 0

Subproblem 1
Set the factor '(-3 + -2X2)' equal to zero and attempt to solve:

Simplifying
-3 + -2X2 = 0

Solving
-3 + -2X2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2X2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2X2 = 0 + 3
-2X2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2X2 = 3

Divide each side by '-2'.
X2 = -1.5

Simplifying
X2 = -1.5

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 '(6 + -1X2)' equal to zero and attempt to solve:

Simplifying
6 + -1X2 = 0

Solving
6 + -1X2 = 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 + -1X2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1X2 = 0 + -6
-1X2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1X2 = -6

Divide each side by '-1'.
X2 = 6

Simplifying
X2 = 6

Take the square root of each side:
X = {-2.449489743, 2.449489743}
Solution
X = {-2.449489743, 2.449489743}