4x^2+6x^4+2=0

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Solution for 4x^2+6x^4+2=0 equation: 


Simplifying
4x2 + 6x4 + 2 = 0

Reorder the terms:
2 + 4x2 + 6x4 = 0

Solving
2 + 4x2 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2x2 + 3x4) = 0

Ignore the factor 2.

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

Simplifying
1 + 2x2 + 3x4 = 0

Solving
1 + 2x2 + 3x4 = 0

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

Divide each side by '3'.
0.3333333333 + 0.6666666667x2 + x4 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.6666666667x2 + -0.3333333333 + x4 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.6666666667x2 + x4 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.6666666667x2 + x4 = 0 + -0.3333333333
0.6666666667x2 + x4 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.6666666667x2 + x4 = -0.3333333333

The x term is 0.6666666667x2.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x2 + 0.1111111112 + x4 = -0.3333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x2 + x4 = -0.3333333333 + 0.1111111112

Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221
0.1111111112 + 0.6666666667x2 + x4 = -0.2222222221

Factor a perfect square on the left side:
(x2 + 0.3333333334)(x2 + 0.3333333334) = -0.2222222221

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.

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