-14x^4-36x^2+54=0

Solution for -14x^4-36x^2+54=0 equation:

Simplifying
-14x4 + -36x2 + 54 = 0

Reorder the terms:
54 + -36x2 + -14x4 = 0

Solving
54 + -36x2 + -14x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -18x2 + -7x4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(27 + -18x2 + -7x4)' equal to zero and attempt to solve:

Simplifying
27 + -18x2 + -7x4 = 0

Solving
27 + -18x2 + -7x4 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-3.857142857 + 2.571428571x2 + x4 = 0

Move the constant term to the right:

Add '3.857142857' to each side of the equation.
-3.857142857 + 2.571428571x2 + 3.857142857 + x4 = 0 + 3.857142857

Reorder the terms:
-3.857142857 + 3.857142857 + 2.571428571x2 + x4 = 0 + 3.857142857

Combine like terms: -3.857142857 + 3.857142857 = 0.000000000
0.000000000 + 2.571428571x2 + x4 = 0 + 3.857142857
2.571428571x2 + x4 = 0 + 3.857142857

Combine like terms: 0 + 3.857142857 = 3.857142857
2.571428571x2 + x4 = 3.857142857

The x term is 2.571428571x2.  Take half its coefficient (1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
2.571428571x2 + 1.653061225 + x4 = 3.857142857 + 1.653061225

Reorder the terms:
1.653061225 + 2.571428571x2 + x4 = 3.857142857 + 1.653061225

Combine like terms: 3.857142857 + 1.653061225 = 5.510204082
1.653061225 + 2.571428571x2 + x4 = 5.510204082

Factor a perfect square on the left side:
(x2 + 1.285714286)(x2 + 1.285714286) = 5.510204082

Calculate the square root of the right side: 2.347382389

Break this problem into two subproblems by setting 
(x2 + 1.285714286) equal to 2.347382389 and -2.347382389.

Subproblem 1
x2 + 1.285714286 = 2.347382389

Simplifying
x2 + 1.285714286 = 2.347382389

Reorder the terms:
1.285714286 + x2 = 2.347382389

Solving
1.285714286 + x2 = 2.347382389

Solving for variable 'x'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + x2 = 2.347382389 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + x2 = 2.347382389 + -1.285714286
x2 = 2.347382389 + -1.285714286

Combine like terms: 2.347382389 + -1.285714286 = 1.061668103
x2 = 1.061668103

Simplifying
x2 = 1.061668103

Take the square root of each side:
x = {-1.030372798, 1.030372798}

Subproblem 2
x2 + 1.285714286 = -2.347382389

Simplifying
x2 + 1.285714286 = -2.347382389

Reorder the terms:
1.285714286 + x2 = -2.347382389

Solving
1.285714286 + x2 = -2.347382389

Solving for variable 'x'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + x2 = -2.347382389 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + x2 = -2.347382389 + -1.285714286
x2 = -2.347382389 + -1.285714286

Combine like terms: -2.347382389 + -1.285714286 = -3.633096675
x2 = -3.633096675

Simplifying
x2 = -3.633096675

Reorder the terms:
3.633096675 + x2 = -3.633096675 + 3.633096675

Combine like terms: -3.633096675 + 3.633096675 = 0.000000000
3.633096675 + x2 = 0.000000000

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.

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

The solution to this equation could not be determined.