18x^4+36x^2+54=0

Solution for 18x^4+36x^2+54=0 equation:

Simplifying
18x4 + 36x2 + 54 = 0

Reorder the terms:
54 + 36x2 + 18x4 = 0

Solving
54 + 36x2 + 18x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '18'.
18(3 + 2x2 + x4) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(3 + 2x2 + x4)' equal to zero and attempt to solve:

Simplifying
3 + 2x2 + x4 = 0

Solving
3 + 2x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2x2 + -3 + x4 = 0 + -3

Reorder the terms:
3 + -3 + 2x2 + x4 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x2 + x4 = 0 + -3
2x2 + x4 = 0 + -3

Combine like terms: 0 + -3 = -3
2x2 + x4 = -3

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = -3 + 1

Reorder the terms:
1 + 2x2 + x4 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2x2 + x4 = -2

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.