3x^8+48x^4+16=0

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Solution for 3x^8+48x^4+16=0 equation: 


Simplifying
3x8 + 48x4 + 16 = 0

Reorder the terms:
16 + 48x4 + 3x8 = 0

Solving
16 + 48x4 + 3x8 = 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'.
5.333333333 + 16x4 + x8 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + 16x4 + -5.333333333 + x8 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + 16x4 + x8 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + 16x4 + x8 = 0 + -5.333333333
16x4 + x8 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
16x4 + x8 = -5.333333333

The x term is 16x4.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x4 + 64 + x8 = -5.333333333 + 64

Reorder the terms:
64 + 16x4 + x8 = -5.333333333 + 64

Combine like terms: -5.333333333 + 64 = 58.666666667
64 + 16x4 + x8 = 58.666666667

Factor a perfect square on the left side:
(x4 + 8)(x4 + 8) = 58.666666667

Calculate the square root of the right side: 7.659416862

Break this problem into two subproblems by setting 
(x4 + 8) equal to 7.659416862 and -7.659416862.


Subproblem 1
x4 + 8 = 7.659416862

Simplifying
x4 + 8 = 7.659416862

Reorder the terms:
8 + x4 = 7.659416862

Solving
8 + x4 = 7.659416862

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x4 = 7.659416862 + -8

Combine like terms: 8 + -8 = 0
0 + x4 = 7.659416862 + -8
x4 = 7.659416862 + -8

Combine like terms: 7.659416862 + -8 = -0.340583138
x4 = -0.340583138

Simplifying
x4 = -0.340583138

Reorder the terms:
0.340583138 + x4 = -0.340583138 + 0.340583138

Combine like terms: -0.340583138 + 0.340583138 = 0.000000000
0.340583138 + x4 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
x4 + 8 = -7.659416862

Simplifying
x4 + 8 = -7.659416862

Reorder the terms:
8 + x4 = -7.659416862

Solving
8 + x4 = -7.659416862

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x4 = -7.659416862 + -8

Combine like terms: 8 + -8 = 0
0 + x4 = -7.659416862 + -8
x4 = -7.659416862 + -8

Combine like terms: -7.659416862 + -8 = -15.659416862
x4 = -15.659416862

Simplifying
x4 = -15.659416862

Reorder the terms:
15.659416862 + x4 = -15.659416862 + 15.659416862

Combine like terms: -15.659416862 + 15.659416862 = 0.000000000
15.659416862 + x4 = 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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