3x^4-32x^2-192=0

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Solution for 3x^4-32x^2-192=0 equation: 


Simplifying
3x4 + -32x2 + -192 = 0

Reorder the terms:
-192 + -32x2 + 3x4 = 0

Solving
-192 + -32x2 + 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'.
-64 + -10.66666667x2 + x4 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -10.66666667x2 + 64 + x4 = 0 + 64

Reorder the terms:
-64 + 64 + -10.66666667x2 + x4 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -10.66666667x2 + x4 = 0 + 64
-10.66666667x2 + x4 = 0 + 64

Combine like terms: 0 + 64 = 64
-10.66666667x2 + x4 = 64

The x term is -10.66666667x2.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x2 + 28.44444446 + x4 = 64 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x2 + x4 = 64 + 28.44444446

Combine like terms: 64 + 28.44444446 = 92.44444446
28.44444446 + -10.66666667x2 + x4 = 92.44444446

Factor a perfect square on the left side:
(x2 + -5.333333335)(x2 + -5.333333335) = 92.44444446

Calculate the square root of the right side: 9.614803402

Break this problem into two subproblems by setting 
(x2 + -5.333333335) equal to 9.614803402 and -9.614803402.


Subproblem 1
x2 + -5.333333335 = 9.614803402

Simplifying
x2 + -5.333333335 = 9.614803402

Reorder the terms:
-5.333333335 + x2 = 9.614803402

Solving
-5.333333335 + x2 = 9.614803402

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x2 = 9.614803402 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x2 = 9.614803402 + 5.333333335
x2 = 9.614803402 + 5.333333335

Combine like terms: 9.614803402 + 5.333333335 = 14.948136737
x2 = 14.948136737

Simplifying
x2 = 14.948136737

Take the square root of each side:
x = {-3.86628203, 3.86628203}


Subproblem 2
x2 + -5.333333335 = -9.614803402

Simplifying
x2 + -5.333333335 = -9.614803402

Reorder the terms:
-5.333333335 + x2 = -9.614803402

Solving
-5.333333335 + x2 = -9.614803402

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x2 = -9.614803402 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x2 = -9.614803402 + 5.333333335
x2 = -9.614803402 + 5.333333335

Combine like terms: -9.614803402 + 5.333333335 = -4.281470067
x2 = -4.281470067

Simplifying
x2 = -4.281470067

Reorder the terms:
4.281470067 + x2 = -4.281470067 + 4.281470067

Combine like terms: -4.281470067 + 4.281470067 = 0.000000000
4.281470067 + 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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