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

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

Simplifying
0 = x4 + 4x2 + -3

Reorder the terms:
0 = -3 + 4x2 + x4

Solving
0 = -3 + 4x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -4x2 + -1x4 = -3 + 4x2 + x4 + 3 + -4x2 + -1x4

Reorder the terms:
3 + -4x2 + -1x4 = -3 + 3 + 4x2 + -4x2 + x4 + -1x4

Combine like terms: -3 + 3 = 0
3 + -4x2 + -1x4 = 0 + 4x2 + -4x2 + x4 + -1x4
3 + -4x2 + -1x4 = 4x2 + -4x2 + x4 + -1x4

Combine like terms: 4x2 + -4x2 = 0
3 + -4x2 + -1x4 = 0 + x4 + -1x4
3 + -4x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
3 + -4x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 4x2 + x4 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4x2 + 3 + x4 = 0 + 3

Reorder the terms:
-3 + 3 + 4x2 + x4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4x2 + x4 = 0 + 3
4x2 + x4 = 0 + 3

Combine like terms: 0 + 3 = 3
4x2 + x4 = 3

The x term is 4x2.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x2 + 4 + x4 = 3 + 4

Reorder the terms:
4 + 4x2 + x4 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + 4x2 + x4 = 7

Factor a perfect square on the left side:
(x2 + 2)(x2 + 2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x2 + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1
x2 + 2 = 2.645751311

Simplifying
x2 + 2 = 2.645751311

Reorder the terms:
2 + x2 = 2.645751311

Solving
2 + x2 = 2.645751311

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x2 = 2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 2.645751311 + -2
x2 = 2.645751311 + -2

Combine like terms: 2.645751311 + -2 = 0.645751311
x2 = 0.645751311

Simplifying
x2 = 0.645751311

Take the square root of each side:
x = {-0.80358653, 0.80358653}

Subproblem 2
x2 + 2 = -2.645751311

Simplifying
x2 + 2 = -2.645751311

Reorder the terms:
2 + x2 = -2.645751311

Solving
2 + x2 = -2.645751311

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x2 = -2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = -2.645751311 + -2
x2 = -2.645751311 + -2

Combine like terms: -2.645751311 + -2 = -4.645751311
x2 = -4.645751311

Simplifying
x2 = -4.645751311

Reorder the terms:
4.645751311 + x2 = -4.645751311 + 4.645751311

Combine like terms: -4.645751311 + 4.645751311 = 0.000000000
4.645751311 + 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.