2x^4-3x^2-1=0

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Solution for 2x^4-3x^2-1=0 equation: 


Simplifying
2x4 + -3x2 + -1 = 0

Reorder the terms:
-1 + -3x2 + 2x4 = 0

Solving
-1 + -3x2 + 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'.
-0.5 + -1.5x2 + x4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.5x2 + 0.5 + x4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.5x2 + x4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.5x2 + x4 = 0 + 0.5
-1.5x2 + x4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.5x2 + x4 = 0.5

The x term is -1.5x2.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x2 + 0.5625 + x4 = 0.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x2 + x4 = 0.5 + 0.5625

Combine like terms: 0.5 + 0.5625 = 1.0625
0.5625 + -1.5x2 + x4 = 1.0625

Factor a perfect square on the left side:
(x2 + -0.75)(x2 + -0.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x2 + -0.75) equal to 1.030776406 and -1.030776406.


Subproblem 1
x2 + -0.75 = 1.030776406

Simplifying
x2 + -0.75 = 1.030776406

Reorder the terms:
-0.75 + x2 = 1.030776406

Solving
-0.75 + x2 = 1.030776406

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x2 = 1.030776406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x2 = 1.030776406 + 0.75
x2 = 1.030776406 + 0.75

Combine like terms: 1.030776406 + 0.75 = 1.780776406
x2 = 1.780776406

Simplifying
x2 = 1.780776406

Take the square root of each side:
x = {-1.334457345, 1.334457345}


Subproblem 2
x2 + -0.75 = -1.030776406

Simplifying
x2 + -0.75 = -1.030776406

Reorder the terms:
-0.75 + x2 = -1.030776406

Solving
-0.75 + x2 = -1.030776406

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x2 = -1.030776406 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x2 = -1.030776406 + 0.75
x2 = -1.030776406 + 0.75

Combine like terms: -1.030776406 + 0.75 = -0.280776406
x2 = -0.280776406

Simplifying
x2 = -0.280776406

Reorder the terms:
0.280776406 + x2 = -0.280776406 + 0.280776406

Combine like terms: -0.280776406 + 0.280776406 = 0.000000000
0.280776406 + 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.

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