9x^6+16x^4+x^2=0

Solution for 9x^6+16x^4+x^2=0 equation:

Simplifying
9x6 + 16x4 + x2 = 0

Reorder the terms:
x2 + 16x4 + 9x6 = 0

Solving
x2 + 16x4 + 9x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + 16x2 + 9x4) = 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 + 16x2 + 9x4)' equal to zero and attempt to solve:

Simplifying
1 + 16x2 + 9x4 = 0

Solving
1 + 16x2 + 9x4 = 0

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

Divide each side by '9'.
0.1111111111 + 1.777777778x2 + x4 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 1.777777778x2 + -0.1111111111 + x4 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 1.777777778x2 + x4 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 1.777777778x2 + x4 = 0 + -0.1111111111
1.777777778x2 + x4 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
1.777777778x2 + x4 = -0.1111111111

The x term is 1.777777778x2.  Take half its coefficient (0.888888889).
Square it (0.7901234570) and add it to both sides.

Add '0.7901234570' to each side of the equation.
1.777777778x2 + 0.7901234570 + x4 = -0.1111111111 + 0.7901234570

Reorder the terms:
0.7901234570 + 1.777777778x2 + x4 = -0.1111111111 + 0.7901234570

Combine like terms: -0.1111111111 + 0.7901234570 = 0.6790123459
0.7901234570 + 1.777777778x2 + x4 = 0.6790123459

Factor a perfect square on the left side:
(x2 + 0.888888889)(x2 + 0.888888889) = 0.6790123459

Calculate the square root of the right side: 0.824022054

Break this problem into two subproblems by setting 
(x2 + 0.888888889) equal to 0.824022054 and -0.824022054.

Subproblem 1
x2 + 0.888888889 = 0.824022054

Simplifying
x2 + 0.888888889 = 0.824022054

Reorder the terms:
0.888888889 + x2 = 0.824022054

Solving
0.888888889 + x2 = 0.824022054

Solving for variable 'x'.

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

Add '-0.888888889' to each side of the equation.
0.888888889 + -0.888888889 + x2 = 0.824022054 + -0.888888889

Combine like terms: 0.888888889 + -0.888888889 = 0.000000000
0.000000000 + x2 = 0.824022054 + -0.888888889
x2 = 0.824022054 + -0.888888889

Combine like terms: 0.824022054 + -0.888888889 = -0.064866835
x2 = -0.064866835

Simplifying
x2 = -0.064866835

Reorder the terms:
0.064866835 + x2 = -0.064866835 + 0.064866835

Combine like terms: -0.064866835 + 0.064866835 = 0.000000000
0.064866835 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2
x2 + 0.888888889 = -0.824022054

Simplifying
x2 + 0.888888889 = -0.824022054

Reorder the terms:
0.888888889 + x2 = -0.824022054

Solving
0.888888889 + x2 = -0.824022054

Solving for variable 'x'.

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

Add '-0.888888889' to each side of the equation.
0.888888889 + -0.888888889 + x2 = -0.824022054 + -0.888888889

Combine like terms: 0.888888889 + -0.888888889 = 0.000000000
0.000000000 + x2 = -0.824022054 + -0.888888889
x2 = -0.824022054 + -0.888888889

Combine like terms: -0.824022054 + -0.888888889 = -1.712910943
x2 = -1.712910943

Simplifying
x2 = -1.712910943

Reorder the terms:
1.712910943 + x2 = -1.712910943 + 1.712910943

Combine like terms: -1.712910943 + 1.712910943 = 0.000000000
1.712910943 + x2 = 0.000000000

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}