x^6-47x^3-8=0

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Solution for x^6-47x^3-8=0 equation: 


Simplifying
x6 + -47x3 + -8 = 0

Reorder the terms:
-8 + -47x3 + x6 = 0

Solving
-8 + -47x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -47x3 + 8 + x6 = 0 + 8

Reorder the terms:
-8 + 8 + -47x3 + x6 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -47x3 + x6 = 0 + 8
-47x3 + x6 = 0 + 8

Combine like terms: 0 + 8 = 8
-47x3 + x6 = 8

The x term is -47x3.  Take half its coefficient (-23.5).
Square it (552.25) and add it to both sides.

Add '552.25' to each side of the equation.
-47x3 + 552.25 + x6 = 8 + 552.25

Reorder the terms:
552.25 + -47x3 + x6 = 8 + 552.25

Combine like terms: 8 + 552.25 = 560.25
552.25 + -47x3 + x6 = 560.25

Factor a perfect square on the left side:
(x3 + -23.5)(x3 + -23.5) = 560.25

Calculate the square root of the right side: 23.669600757

Break this problem into two subproblems by setting 
(x3 + -23.5) equal to 23.669600757 and -23.669600757.


Subproblem 1
x3 + -23.5 = 23.669600757

Simplifying
x3 + -23.5 = 23.669600757

Reorder the terms:
-23.5 + x3 = 23.669600757

Solving
-23.5 + x3 = 23.669600757

Solving for variable 'x'.

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

Add '23.5' to each side of the equation.
-23.5 + 23.5 + x3 = 23.669600757 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + x3 = 23.669600757 + 23.5
x3 = 23.669600757 + 23.5

Combine like terms: 23.669600757 + 23.5 = 47.169600757
x3 = 47.169600757

Simplifying
x3 = 47.169600757

Reorder the terms:
-47.169600757 + x3 = 47.169600757 + -47.169600757

Combine like terms: 47.169600757 + -47.169600757 = 0.000000000
-47.169600757 + x3 = 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
x3 + -23.5 = -23.669600757

Simplifying
x3 + -23.5 = -23.669600757

Reorder the terms:
-23.5 + x3 = -23.669600757

Solving
-23.5 + x3 = -23.669600757

Solving for variable 'x'.

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

Add '23.5' to each side of the equation.
-23.5 + 23.5 + x3 = -23.669600757 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + x3 = -23.669600757 + 23.5
x3 = -23.669600757 + 23.5

Combine like terms: -23.669600757 + 23.5 = -0.169600757
x3 = -0.169600757

Simplifying
x3 = -0.169600757

Reorder the terms:
0.169600757 + x3 = -0.169600757 + 0.169600757

Combine like terms: -0.169600757 + 0.169600757 = 0.000000000
0.169600757 + x3 = 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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