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

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

Simplifying
2x4 + -9x2 + 2 = 0

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

Solving
2 + -9x2 + 2x4 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
1 + -4.5x2 + x4 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4.5x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -4.5x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4.5x2 + x4 = 0 + -1
-4.5x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-4.5x2 + x4 = -1

The x term is -4.5x2.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x2 + 5.0625 + x4 = -1 + 5.0625

Reorder the terms:
5.0625 + -4.5x2 + x4 = -1 + 5.0625

Combine like terms: -1 + 5.0625 = 4.0625
5.0625 + -4.5x2 + x4 = 4.0625

Factor a perfect square on the left side:
(x2 + -2.25)(x2 + -2.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x2 + -2.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
x2 + -2.25 = 2.015564437

Simplifying
x2 + -2.25 = 2.015564437

Reorder the terms:
-2.25 + x2 = 2.015564437

Solving
-2.25 + x2 = 2.015564437

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x2 = 2.015564437 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x2 = 2.015564437 + 2.25
x2 = 2.015564437 + 2.25

Combine like terms: 2.015564437 + 2.25 = 4.265564437
x2 = 4.265564437

Simplifying
x2 = 4.265564437

Take the square root of each side:
x = {-2.065324293, 2.065324293}

Subproblem 2
x2 + -2.25 = -2.015564437

Simplifying
x2 + -2.25 = -2.015564437

Reorder the terms:
-2.25 + x2 = -2.015564437

Solving
-2.25 + x2 = -2.015564437

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x2 = -2.015564437 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x2 = -2.015564437 + 2.25
x2 = -2.015564437 + 2.25

Combine like terms: -2.015564437 + 2.25 = 0.234435563
x2 = 0.234435563

Simplifying
x2 = 0.234435563

Take the square root of each side:
x = {-0.484185463, 0.484185463}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.065324293, 2.065324293, -0.484185463, 0.484185463}