n^6-24n^3-8=

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Solution for n^6-24n^3-8= equation: 


Simplifying
n6 + -24n3 + -8 = 0

Reorder the terms:
-8 + -24n3 + n6 = 0

Solving
-8 + -24n3 + n6 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -24n3 + 8 + n6 = 0 + 8

Reorder the terms:
-8 + 8 + -24n3 + n6 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -24n3 + n6 = 0 + 8
-24n3 + n6 = 0 + 8

Combine like terms: 0 + 8 = 8
-24n3 + n6 = 8

The n term is -24n3.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24n3 + 144 + n6 = 8 + 144

Reorder the terms:
144 + -24n3 + n6 = 8 + 144

Combine like terms: 8 + 144 = 152
144 + -24n3 + n6 = 152

Factor a perfect square on the left side:
(n3 + -12)(n3 + -12) = 152

Calculate the square root of the right side: 12.328828006

Break this problem into two subproblems by setting 
(n3 + -12) equal to 12.328828006 and -12.328828006.


Subproblem 1
n3 + -12 = 12.328828006

Simplifying
n3 + -12 = 12.328828006

Reorder the terms:
-12 + n3 = 12.328828006

Solving
-12 + n3 = 12.328828006

Solving for variable 'n'.

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

Add '12' to each side of the equation.
-12 + 12 + n3 = 12.328828006 + 12

Combine like terms: -12 + 12 = 0
0 + n3 = 12.328828006 + 12
n3 = 12.328828006 + 12

Combine like terms: 12.328828006 + 12 = 24.328828006
n3 = 24.328828006

Simplifying
n3 = 24.328828006

Reorder the terms:
-24.328828006 + n3 = 24.328828006 + -24.328828006

Combine like terms: 24.328828006 + -24.328828006 = 0.000000000
-24.328828006 + n3 = 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
n3 + -12 = -12.328828006

Simplifying
n3 + -12 = -12.328828006

Reorder the terms:
-12 + n3 = -12.328828006

Solving
-12 + n3 = -12.328828006

Solving for variable 'n'.

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

Add '12' to each side of the equation.
-12 + 12 + n3 = -12.328828006 + 12

Combine like terms: -12 + 12 = 0
0 + n3 = -12.328828006 + 12
n3 = -12.328828006 + 12

Combine like terms: -12.328828006 + 12 = -0.328828006
n3 = -0.328828006

Simplifying
n3 = -0.328828006

Reorder the terms:
0.328828006 + n3 = -0.328828006 + 0.328828006

Combine like terms: -0.328828006 + 0.328828006 = 0.000000000
0.328828006 + n3 = 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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