x^2-2x^4+10x^6=0

Solution for x^2-2x^4+10x^6=0 equation:

Simplifying
x2 + -2x4 + 10x6 = 0

Solving
x2 + -2x4 + 10x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + -2x2 + 10x4) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + -2x2 + 10x4)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 + 10x4 = 0

Solving
1 + -2x2 + 10x4 = 0

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

Divide each side by '10'.
0.1 + -0.2x2 + x4 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -0.2x2 + -0.1 + x4 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + -0.2x2 + x4 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -0.2x2 + x4 = 0 + -0.1
-0.2x2 + x4 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
-0.2x2 + x4 = -0.1

The x term is -0.2x2.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x2 + 0.01 + x4 = -0.1 + 0.01

Reorder the terms:
0.01 + -0.2x2 + x4 = -0.1 + 0.01

Combine like terms: -0.1 + 0.01 = -0.09
0.01 + -0.2x2 + x4 = -0.09

Factor a perfect square on the left side:
(x2 + -0.1)(x2 + -0.1) = -0.09

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.
Solution
x = {0}