5x^4-10x^2+2=0

Solution for 5x^4-10x^2+2=0 equation:

Simplifying
5x4 + -10x2 + 2 = 0

Reorder the terms:
2 + -10x2 + 5x4 = 0

Solving
2 + -10x2 + 5x4 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.4 + -2x2 + x4 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2x2 + -0.4 + x4 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2x2 + x4 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2x2 + x4 = 0 + -0.4
-2x2 + x4 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2x2 + x4 = -0.4

The x term is -2x2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x2 + 1 + x4 = -0.4 + 1

Reorder the terms:
1 + -2x2 + x4 = -0.4 + 1

Combine like terms: -0.4 + 1 = 0.6
1 + -2x2 + x4 = 0.6

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 0.6

Calculate the square root of the right side: 0.774596669

Break this problem into two subproblems by setting 
(x2 + -1) equal to 0.774596669 and -0.774596669.

Subproblem 1
x2 + -1 = 0.774596669

Simplifying
x2 + -1 = 0.774596669

Reorder the terms:
-1 + x2 = 0.774596669

Solving
-1 + x2 = 0.774596669

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = 0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = 0.774596669 + 1
x2 = 0.774596669 + 1

Combine like terms: 0.774596669 + 1 = 1.774596669
x2 = 1.774596669

Simplifying
x2 = 1.774596669

Take the square root of each side:
x = {-1.332139883, 1.332139883}

Subproblem 2
x2 + -1 = -0.774596669

Simplifying
x2 + -1 = -0.774596669

Reorder the terms:
-1 + x2 = -0.774596669

Solving
-1 + x2 = -0.774596669

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x2 = -0.774596669 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = -0.774596669 + 1
x2 = -0.774596669 + 1

Combine like terms: -0.774596669 + 1 = 0.225403331
x2 = 0.225403331

Simplifying
x2 = 0.225403331

Take the square root of each side:
x = {-0.474766607, 0.474766607}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.332139883, 1.332139883, -0.474766607, 0.474766607}