2x^4=3-8x^2

Solution for 2x^4=3-8x^2 equation:

Simplifying
2x4 = 3 + -8x2

Solving
2x4 = 3 + -8x2

Solving for variable 'x'.

Reorder the terms:
-3 + 8x2 + 2x4 = 3 + -8x2 + -3 + 8x2

Reorder the terms:
-3 + 8x2 + 2x4 = 3 + -3 + -8x2 + 8x2

Combine like terms: 3 + -3 = 0
-3 + 8x2 + 2x4 = 0 + -8x2 + 8x2
-3 + 8x2 + 2x4 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-3 + 8x2 + 2x4 = 0

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

Divide each side by '2'.
-1.5 + 4x2 + x4 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4x2 + 1.5 + x4 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4x2 + x4 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4x2 + x4 = 0 + 1.5
4x2 + x4 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4x2 + x4 = 1.5

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 = 1.5 + 4

Reorder the terms:
4 + 4x2 + x4 = 1.5 + 4

Combine like terms: 1.5 + 4 = 5.5
4 + 4x2 + x4 = 5.5

Factor a perfect square on the left side:
(x2 + 2)(x2 + 2) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x2 + 2) equal to 2.34520788 and -2.34520788.

Subproblem 1
x2 + 2 = 2.34520788

Simplifying
x2 + 2 = 2.34520788

Reorder the terms:
2 + x2 = 2.34520788

Solving
2 + x2 = 2.34520788

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 = 2.34520788 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = 2.34520788 + -2
x2 = 2.34520788 + -2

Combine like terms: 2.34520788 + -2 = 0.34520788
x2 = 0.34520788

Simplifying
x2 = 0.34520788

Take the square root of each side:
x = {-0.587543939, 0.587543939}

Subproblem 2
x2 + 2 = -2.34520788

Simplifying
x2 + 2 = -2.34520788

Reorder the terms:
2 + x2 = -2.34520788

Solving
2 + x2 = -2.34520788

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 = -2.34520788 + -2

Combine like terms: 2 + -2 = 0
0 + x2 = -2.34520788 + -2
x2 = -2.34520788 + -2

Combine like terms: -2.34520788 + -2 = -4.34520788
x2 = -4.34520788

Simplifying
x2 = -4.34520788

Reorder the terms:
4.34520788 + x2 = -4.34520788 + 4.34520788

Combine like terms: -4.34520788 + 4.34520788 = 0.00000000
4.34520788 + x2 = 0.00000000

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.