3*x^4+2*x^2-240=0

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Solution for 3*x^4+2*x^2-240=0 equation: 


Simplifying
3x4 + 2x2 + -240 = 0

Reorder the terms:
-240 + 2x2 + 3x4 = 0

Solving
-240 + 2x2 + 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'.
-80 + 0.6666666667x2 + x4 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 0.6666666667x2 + 80 + x4 = 0 + 80

Reorder the terms:
-80 + 80 + 0.6666666667x2 + x4 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 0.6666666667x2 + x4 = 0 + 80
0.6666666667x2 + x4 = 0 + 80

Combine like terms: 0 + 80 = 80
0.6666666667x2 + x4 = 80

The x term is 0.6666666667x2.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x2 + 0.1111111112 + x4 = 80 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x2 + x4 = 80 + 0.1111111112

Combine like terms: 80 + 0.1111111112 = 80.1111111112
0.1111111112 + 0.6666666667x2 + x4 = 80.1111111112

Factor a perfect square on the left side:
(x2 + 0.3333333334)(x2 + 0.3333333334) = 80.1111111112

Calculate the square root of the right side: 8.950481055

Break this problem into two subproblems by setting 
(x2 + 0.3333333334) equal to 8.950481055 and -8.950481055.


Subproblem 1
x2 + 0.3333333334 = 8.950481055

Simplifying
x2 + 0.3333333334 = 8.950481055

Reorder the terms:
0.3333333334 + x2 = 8.950481055

Solving
0.3333333334 + x2 = 8.950481055

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x2 = 8.950481055 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x2 = 8.950481055 + -0.3333333334
x2 = 8.950481055 + -0.3333333334

Combine like terms: 8.950481055 + -0.3333333334 = 8.6171477216
x2 = 8.6171477216

Simplifying
x2 = 8.6171477216

Take the square root of each side:
x = {-2.935497866, 2.935497866}


Subproblem 2
x2 + 0.3333333334 = -8.950481055

Simplifying
x2 + 0.3333333334 = -8.950481055

Reorder the terms:
0.3333333334 + x2 = -8.950481055

Solving
0.3333333334 + x2 = -8.950481055

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x2 = -8.950481055 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x2 = -8.950481055 + -0.3333333334
x2 = -8.950481055 + -0.3333333334

Combine like terms: -8.950481055 + -0.3333333334 = -9.2838143884
x2 = -9.2838143884

Simplifying
x2 = -9.2838143884

Reorder the terms:
9.2838143884 + x2 = -9.2838143884 + 9.2838143884

Combine like terms: -9.2838143884 + 9.2838143884 = 0.0000000000
9.2838143884 + x2 = 0.0000000000

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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