5x^4+10x^2+1=0

Solution for 5x^4+10x^2+1=0 equation:

Simplifying
5x4 + 10x2 + 1 = 0

Reorder the terms:
1 + 10x2 + 5x4 = 0

Solving
1 + 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'.
0.2 + 2x2 + x4 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2x2 + -0.2 + x4 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2x2 + x4 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2x2 + x4 = 0 + -0.2
2x2 + x4 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2x2 + x4 = -0.2

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 = -0.2 + 1

Reorder the terms:
1 + 2x2 + x4 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + 2x2 + x4 = 0.8

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
(x2 + 1) equal to 0.894427191 and -0.894427191.

Subproblem 1
x2 + 1 = 0.894427191

Simplifying
x2 + 1 = 0.894427191

Reorder the terms:
1 + x2 = 0.894427191

Solving
1 + x2 = 0.894427191

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 = 0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0.894427191 + -1
x2 = 0.894427191 + -1

Combine like terms: 0.894427191 + -1 = -0.105572809
x2 = -0.105572809

Simplifying
x2 = -0.105572809

Reorder the terms:
0.105572809 + x2 = -0.105572809 + 0.105572809

Combine like terms: -0.105572809 + 0.105572809 = 0.000000000
0.105572809 + 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 + 1 = -0.894427191

Simplifying
x2 + 1 = -0.894427191

Reorder the terms:
1 + x2 = -0.894427191

Solving
1 + x2 = -0.894427191

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 = -0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = -0.894427191 + -1
x2 = -0.894427191 + -1

Combine like terms: -0.894427191 + -1 = -1.894427191
x2 = -1.894427191

Simplifying
x2 = -1.894427191

Reorder the terms:
1.894427191 + x2 = -1.894427191 + 1.894427191

Combine like terms: -1.894427191 + 1.894427191 = 0.000000000
1.894427191 + 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.