0=9x^4-20x^2+9

Solution for 0=9x^4-20x^2+9 equation:

Simplifying
0 = 9x4 + -20x2 + 9

Reorder the terms:
0 = 9 + -20x2 + 9x4

Solving
0 = 9 + -20x2 + 9x4

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + 20x2 + -9x4 = 9 + -20x2 + 9x4 + -9 + 20x2 + -9x4

Reorder the terms:
-9 + 20x2 + -9x4 = 9 + -9 + -20x2 + 20x2 + 9x4 + -9x4

Combine like terms: 9 + -9 = 0
-9 + 20x2 + -9x4 = 0 + -20x2 + 20x2 + 9x4 + -9x4
-9 + 20x2 + -9x4 = -20x2 + 20x2 + 9x4 + -9x4

Combine like terms: -20x2 + 20x2 = 0
-9 + 20x2 + -9x4 = 0 + 9x4 + -9x4
-9 + 20x2 + -9x4 = 9x4 + -9x4

Combine like terms: 9x4 + -9x4 = 0
-9 + 20x2 + -9x4 = 0

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

Divide each side by '-9'.
1 + -2.222222222x2 + x4 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.222222222x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -2.222222222x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.222222222x2 + x4 = 0 + -1
-2.222222222x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.222222222x2 + x4 = -1

The x term is -2.222222222x2.  Take half its coefficient (-1.111111111).
Square it (1.234567901) and add it to both sides.

Add '1.234567901' to each side of the equation.
-2.222222222x2 + 1.234567901 + x4 = -1 + 1.234567901

Reorder the terms:
1.234567901 + -2.222222222x2 + x4 = -1 + 1.234567901

Combine like terms: -1 + 1.234567901 = 0.234567901
1.234567901 + -2.222222222x2 + x4 = 0.234567901

Factor a perfect square on the left side:
(x2 + -1.111111111)(x2 + -1.111111111) = 0.234567901

Calculate the square root of the right side: 0.484322105

Break this problem into two subproblems by setting 
(x2 + -1.111111111) equal to 0.484322105 and -0.484322105.

Subproblem 1
x2 + -1.111111111 = 0.484322105

Simplifying
x2 + -1.111111111 = 0.484322105

Reorder the terms:
-1.111111111 + x2 = 0.484322105

Solving
-1.111111111 + x2 = 0.484322105

Solving for variable 'x'.

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

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.111111111 + x2 = 0.484322105 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + x2 = 0.484322105 + 1.111111111
x2 = 0.484322105 + 1.111111111

Combine like terms: 0.484322105 + 1.111111111 = 1.595433216
x2 = 1.595433216

Simplifying
x2 = 1.595433216

Take the square root of each side:
x = {-1.263104594, 1.263104594}

Subproblem 2
x2 + -1.111111111 = -0.484322105

Simplifying
x2 + -1.111111111 = -0.484322105

Reorder the terms:
-1.111111111 + x2 = -0.484322105

Solving
-1.111111111 + x2 = -0.484322105

Solving for variable 'x'.

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

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.111111111 + x2 = -0.484322105 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + x2 = -0.484322105 + 1.111111111
x2 = -0.484322105 + 1.111111111

Combine like terms: -0.484322105 + 1.111111111 = 0.626789006
x2 = 0.626789006

Simplifying
x2 = 0.626789006

Take the square root of each side:
x = {-0.791700073, 0.791700073}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.263104594, 1.263104594, -0.791700073, 0.791700073}