3x^4-12x^2-2=

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Solution for 3x^4-12x^2-2= equation: 


Simplifying
3x4 + -12x2 + -2 = 0

Reorder the terms:
-2 + -12x2 + 3x4 = 0

Solving
-2 + -12x2 + 3x4 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-0.6666666667 + -4x2 + x4 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4x2 + 0.6666666667 + x4 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4x2 + x4 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4x2 + x4 = 0 + 0.6666666667
-4x2 + x4 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4x2 + x4 = 0.6666666667

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 = 0.6666666667 + 4

Reorder the terms:
4 + -4x2 + x4 = 0.6666666667 + 4

Combine like terms: 0.6666666667 + 4 = 4.6666666667
4 + -4x2 + x4 = 4.6666666667

Factor a perfect square on the left side:
(x2 + -2)(x2 + -2) = 4.6666666667

Calculate the square root of the right side: 2.160246899

Break this problem into two subproblems by setting 
(x2 + -2) equal to 2.160246899 and -2.160246899.


Subproblem 1
x2 + -2 = 2.160246899

Simplifying
x2 + -2 = 2.160246899

Reorder the terms:
-2 + x2 = 2.160246899

Solving
-2 + x2 = 2.160246899

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 = 2.160246899 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = 2.160246899 + 2
x2 = 2.160246899 + 2

Combine like terms: 2.160246899 + 2 = 4.160246899
x2 = 4.160246899

Simplifying
x2 = 4.160246899

Take the square root of each side:
x = {-2.039668331, 2.039668331}


Subproblem 2
x2 + -2 = -2.160246899

Simplifying
x2 + -2 = -2.160246899

Reorder the terms:
-2 + x2 = -2.160246899

Solving
-2 + x2 = -2.160246899

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 = -2.160246899 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = -2.160246899 + 2
x2 = -2.160246899 + 2

Combine like terms: -2.160246899 + 2 = -0.160246899
x2 = -0.160246899

Simplifying
x2 = -0.160246899

Reorder the terms:
0.160246899 + x2 = -0.160246899 + 0.160246899

Combine like terms: -0.160246899 + 0.160246899 = 0.000000000
0.160246899 + 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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