11x^6+03x^4-20x^2+00=0

Solution for 11x^6+03x^4-20x^2+00=0 equation:

Simplifying
11x6 + 3x4 + -20x2 + 0 = 0

Reorder the terms:
0 + -20x2 + 3x4 + 11x6 = 0
Remove the zero:
-20x2 + 3x4 + 11x6 = 0

Solving
-20x2 + 3x4 + 11x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-20 + 3x2 + 11x4) = 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 '(-20 + 3x2 + 11x4)' equal to zero and attempt to solve:

Simplifying
-20 + 3x2 + 11x4 = 0

Solving
-20 + 3x2 + 11x4 = 0

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

Divide each side by '11'.
-1.818181818 + 0.2727272727x2 + x4 = 0

Move the constant term to the right:

Add '1.818181818' to each side of the equation.
-1.818181818 + 0.2727272727x2 + 1.818181818 + x4 = 0 + 1.818181818

Reorder the terms:
-1.818181818 + 1.818181818 + 0.2727272727x2 + x4 = 0 + 1.818181818

Combine like terms: -1.818181818 + 1.818181818 = 0.000000000
0.000000000 + 0.2727272727x2 + x4 = 0 + 1.818181818
0.2727272727x2 + x4 = 0 + 1.818181818

Combine like terms: 0 + 1.818181818 = 1.818181818
0.2727272727x2 + x4 = 1.818181818

The x term is 0.2727272727x2.  Take half its coefficient (0.1363636364).
Square it (0.01859504133) and add it to both sides.

Add '0.01859504133' to each side of the equation.
0.2727272727x2 + 0.01859504133 + x4 = 1.818181818 + 0.01859504133

Reorder the terms:
0.01859504133 + 0.2727272727x2 + x4 = 1.818181818 + 0.01859504133

Combine like terms: 1.818181818 + 0.01859504133 = 1.83677685933
0.01859504133 + 0.2727272727x2 + x4 = 1.83677685933

Factor a perfect square on the left side:
(x2 + 0.1363636364)(x2 + 0.1363636364) = 1.83677685933

Calculate the square root of the right side: 1.35527741

Break this problem into two subproblems by setting 
(x2 + 0.1363636364) equal to 1.35527741 and -1.35527741.

Subproblem 1
x2 + 0.1363636364 = 1.35527741

Simplifying
x2 + 0.1363636364 = 1.35527741

Reorder the terms:
0.1363636364 + x2 = 1.35527741

Solving
0.1363636364 + x2 = 1.35527741

Solving for variable 'x'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + x2 = 1.35527741 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + x2 = 1.35527741 + -0.1363636364
x2 = 1.35527741 + -0.1363636364

Combine like terms: 1.35527741 + -0.1363636364 = 1.2189137736
x2 = 1.2189137736

Simplifying
x2 = 1.2189137736

Take the square root of each side:
x = {-1.104044281, 1.104044281}

Subproblem 2
x2 + 0.1363636364 = -1.35527741

Simplifying
x2 + 0.1363636364 = -1.35527741

Reorder the terms:
0.1363636364 + x2 = -1.35527741

Solving
0.1363636364 + x2 = -1.35527741

Solving for variable 'x'.

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

Add '-0.1363636364' to each side of the equation.
0.1363636364 + -0.1363636364 + x2 = -1.35527741 + -0.1363636364

Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000
0.0000000000 + x2 = -1.35527741 + -0.1363636364
x2 = -1.35527741 + -0.1363636364

Combine like terms: -1.35527741 + -0.1363636364 = -1.4916410464
x2 = -1.4916410464

Simplifying
x2 = -1.4916410464

Reorder the terms:
1.4916410464 + x2 = -1.4916410464 + 1.4916410464

Combine like terms: -1.4916410464 + 1.4916410464 = 0.0000000000
1.4916410464 + x2 = 0.0000000000

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.
Solution
x = {0}