16x^4+4x^2+6=0

Solution for 16x^4+4x^2+6=0 equation:

Simplifying
16x4 + 4x2 + 6 = 0

Reorder the terms:
6 + 4x2 + 16x4 = 0

Solving
6 + 4x2 + 16x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 2x2 + 8x4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 2x2 + 8x4)' equal to zero and attempt to solve:

Simplifying
3 + 2x2 + 8x4 = 0

Solving
3 + 2x2 + 8x4 = 0

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

Divide each side by '8'.
0.375 + 0.25x2 + x4 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 0.25x2 + -0.375 + x4 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 0.25x2 + x4 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 0.25x2 + x4 = 0 + -0.375
0.25x2 + x4 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
0.25x2 + x4 = -0.375

The x term is 0.25x2.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x2 + 0.015625 + x4 = -0.375 + 0.015625

Reorder the terms:
0.015625 + 0.25x2 + x4 = -0.375 + 0.015625

Combine like terms: -0.375 + 0.015625 = -0.359375
0.015625 + 0.25x2 + x4 = -0.359375

Factor a perfect square on the left side:
(x2 + 0.125)(x2 + 0.125) = -0.359375

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.