108x^4-46x^2-8=0

Solution for 108x^4-46x^2-8=0 equation:

Simplifying
108x4 + -46x2 + -8 = 0

Reorder the terms:
-8 + -46x2 + 108x4 = 0

Solving
-8 + -46x2 + 108x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -23x2 + 54x4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -23x2 + 54x4)' equal to zero and attempt to solve:

Simplifying
-4 + -23x2 + 54x4 = 0

Solving
-4 + -23x2 + 54x4 = 0

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

Divide each side by '54'.
-0.07407407407 + -0.4259259259x2 + x4 = 0

Move the constant term to the right:

Add '0.07407407407' to each side of the equation.
-0.07407407407 + -0.4259259259x2 + 0.07407407407 + x4 = 0 + 0.07407407407

Reorder the terms:
-0.07407407407 + 0.07407407407 + -0.4259259259x2 + x4 = 0 + 0.07407407407

Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000
0.00000000000 + -0.4259259259x2 + x4 = 0 + 0.07407407407
-0.4259259259x2 + x4 = 0 + 0.07407407407

Combine like terms: 0 + 0.07407407407 = 0.07407407407
-0.4259259259x2 + x4 = 0.07407407407

The x term is -0.4259259259x2.  Take half its coefficient (-0.212962963).
Square it (0.04535322361) and add it to both sides.

Add '0.04535322361' to each side of the equation.
-0.4259259259x2 + 0.04535322361 + x4 = 0.07407407407 + 0.04535322361

Reorder the terms:
0.04535322361 + -0.4259259259x2 + x4 = 0.07407407407 + 0.04535322361

Combine like terms: 0.07407407407 + 0.04535322361 = 0.11942729768
0.04535322361 + -0.4259259259x2 + x4 = 0.11942729768

Factor a perfect square on the left side:
(x2 + -0.212962963)(x2 + -0.212962963) = 0.11942729768

Calculate the square root of the right side: 0.345582548

Break this problem into two subproblems by setting 
(x2 + -0.212962963) equal to 0.345582548 and -0.345582548.

Subproblem 1
x2 + -0.212962963 = 0.345582548

Simplifying
x2 + -0.212962963 = 0.345582548

Reorder the terms:
-0.212962963 + x2 = 0.345582548

Solving
-0.212962963 + x2 = 0.345582548

Solving for variable 'x'.

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

Add '0.212962963' to each side of the equation.
-0.212962963 + 0.212962963 + x2 = 0.345582548 + 0.212962963

Combine like terms: -0.212962963 + 0.212962963 = 0.000000000
0.000000000 + x2 = 0.345582548 + 0.212962963
x2 = 0.345582548 + 0.212962963

Combine like terms: 0.345582548 + 0.212962963 = 0.558545511
x2 = 0.558545511

Simplifying
x2 = 0.558545511

Take the square root of each side:
x = {-0.747359024, 0.747359024}

Subproblem 2
x2 + -0.212962963 = -0.345582548

Simplifying
x2 + -0.212962963 = -0.345582548

Reorder the terms:
-0.212962963 + x2 = -0.345582548

Solving
-0.212962963 + x2 = -0.345582548

Solving for variable 'x'.

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

Add '0.212962963' to each side of the equation.
-0.212962963 + 0.212962963 + x2 = -0.345582548 + 0.212962963

Combine like terms: -0.212962963 + 0.212962963 = 0.000000000
0.000000000 + x2 = -0.345582548 + 0.212962963
x2 = -0.345582548 + 0.212962963

Combine like terms: -0.345582548 + 0.212962963 = -0.132619585
x2 = -0.132619585

Simplifying
x2 = -0.132619585

Reorder the terms:
0.132619585 + x2 = -0.132619585 + 0.132619585

Combine like terms: -0.132619585 + 0.132619585 = 0.000000000
0.132619585 + 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.