0=9x^4+2x^2-3

Solution for 0=9x^4+2x^2-3 equation:

Simplifying
0 = 9x4 + 2x2 + -3

Reorder the terms:
0 = -3 + 2x2 + 9x4

Solving
0 = -3 + 2x2 + 9x4

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -2x2 + -9x4 = -3 + 2x2 + 9x4 + 3 + -2x2 + -9x4

Reorder the terms:
3 + -2x2 + -9x4 = -3 + 3 + 2x2 + -2x2 + 9x4 + -9x4

Combine like terms: -3 + 3 = 0
3 + -2x2 + -9x4 = 0 + 2x2 + -2x2 + 9x4 + -9x4
3 + -2x2 + -9x4 = 2x2 + -2x2 + 9x4 + -9x4

Combine like terms: 2x2 + -2x2 = 0
3 + -2x2 + -9x4 = 0 + 9x4 + -9x4
3 + -2x2 + -9x4 = 9x4 + -9x4

Combine like terms: 9x4 + -9x4 = 0
3 + -2x2 + -9x4 = 0

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

Divide each side by '-9'.
-0.3333333333 + 0.2222222222x2 + x4 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.2222222222x2 + 0.3333333333 + x4 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.2222222222x2 + x4 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.2222222222x2 + x4 = 0 + 0.3333333333
0.2222222222x2 + x4 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.2222222222x2 + x4 = 0.3333333333

The x term is 0.2222222222x2.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x2 + 0.01234567901 + x4 = 0.3333333333 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x2 + x4 = 0.3333333333 + 0.01234567901

Combine like terms: 0.3333333333 + 0.01234567901 = 0.34567901231
0.01234567901 + 0.2222222222x2 + x4 = 0.34567901231

Factor a perfect square on the left side:
(x2 + 0.1111111111)(x2 + 0.1111111111) = 0.34567901231

Calculate the square root of the right side: 0.587944736

Break this problem into two subproblems by setting 
(x2 + 0.1111111111) equal to 0.587944736 and -0.587944736.

Subproblem 1
x2 + 0.1111111111 = 0.587944736

Simplifying
x2 + 0.1111111111 = 0.587944736

Reorder the terms:
0.1111111111 + x2 = 0.587944736

Solving
0.1111111111 + x2 = 0.587944736

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x2 = 0.587944736 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x2 = 0.587944736 + -0.1111111111
x2 = 0.587944736 + -0.1111111111

Combine like terms: 0.587944736 + -0.1111111111 = 0.4768336249
x2 = 0.4768336249

Simplifying
x2 = 0.4768336249

Take the square root of each side:
x = {-0.690531408, 0.690531408}

Subproblem 2
x2 + 0.1111111111 = -0.587944736

Simplifying
x2 + 0.1111111111 = -0.587944736

Reorder the terms:
0.1111111111 + x2 = -0.587944736

Solving
0.1111111111 + x2 = -0.587944736

Solving for variable 'x'.

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

Add '-0.1111111111' to each side of the equation.
0.1111111111 + -0.1111111111 + x2 = -0.587944736 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x2 = -0.587944736 + -0.1111111111
x2 = -0.587944736 + -0.1111111111

Combine like terms: -0.587944736 + -0.1111111111 = -0.6990558471
x2 = -0.6990558471

Simplifying
x2 = -0.6990558471

Reorder the terms:
0.6990558471 + x2 = -0.6990558471 + 0.6990558471

Combine like terms: -0.6990558471 + 0.6990558471 = 0.0000000000
0.6990558471 + 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.