x^6-10x^3-16=0

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Solution for x^6-10x^3-16=0 equation: 


Simplifying
x6 + -10x3 + -16 = 0

Reorder the terms:
-16 + -10x3 + x6 = 0

Solving
-16 + -10x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -10x3 + 16 + x6 = 0 + 16

Reorder the terms:
-16 + 16 + -10x3 + x6 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -10x3 + x6 = 0 + 16
-10x3 + x6 = 0 + 16

Combine like terms: 0 + 16 = 16
-10x3 + x6 = 16

The x term is -10x3.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x3 + 25 + x6 = 16 + 25

Reorder the terms:
25 + -10x3 + x6 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + -10x3 + x6 = 41

Factor a perfect square on the left side:
(x3 + -5)(x3 + -5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x3 + -5) equal to 6.403124237 and -6.403124237.


Subproblem 1
x3 + -5 = 6.403124237

Simplifying
x3 + -5 = 6.403124237

Reorder the terms:
-5 + x3 = 6.403124237

Solving
-5 + x3 = 6.403124237

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x3 = 6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + x3 = 6.403124237 + 5
x3 = 6.403124237 + 5

Combine like terms: 6.403124237 + 5 = 11.403124237
x3 = 11.403124237

Simplifying
x3 = 11.403124237

Reorder the terms:
-11.403124237 + x3 = 11.403124237 + -11.403124237

Combine like terms: 11.403124237 + -11.403124237 = 0.000000000
-11.403124237 + 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 + -5 = -6.403124237

Simplifying
x3 + -5 = -6.403124237

Reorder the terms:
-5 + x3 = -6.403124237

Solving
-5 + x3 = -6.403124237

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x3 = -6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + x3 = -6.403124237 + 5
x3 = -6.403124237 + 5

Combine like terms: -6.403124237 + 5 = -1.403124237
x3 = -1.403124237

Simplifying
x3 = -1.403124237

Reorder the terms:
1.403124237 + x3 = -1.403124237 + 1.403124237

Combine like terms: -1.403124237 + 1.403124237 = 0.000000000
1.403124237 + 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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