4x^4-2x^2+1=0

Solution for 4x^4-2x^2+1=0 equation:

Simplifying
4x4 + -2x2 + 1 = 0

Reorder the terms:
1 + -2x2 + 4x4 = 0

Solving
1 + -2x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
0.25 + -0.5x2 + x4 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.5x2 + -0.25 + x4 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.5x2 + x4 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.5x2 + x4 = 0 + -0.25
-0.5x2 + x4 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.5x2 + x4 = -0.25

The x term is -0.5x2.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x2 + 0.0625 + x4 = -0.25 + 0.0625

Reorder the terms:
0.0625 + -0.5x2 + x4 = -0.25 + 0.0625

Combine like terms: -0.25 + 0.0625 = -0.1875
0.0625 + -0.5x2 + x4 = -0.1875

Factor a perfect square on the left side:
(x2 + -0.25)(x2 + -0.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.