X^5-X^4-8X^3=0

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Solution for X^5-X^4-8X^3=0 equation: 


Simplifying
X5 + -1X4 + -8X3 = 0

Reorder the terms:
-8X3 + -1X4 + X5 = 0

Solving
-8X3 + -1X4 + X5 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), 'X3'.
X3(-8 + -1X + X2) = 0


Subproblem 1
Set the factor 'X3' equal to zero and attempt to solve:

Simplifying
X3 = 0

Solving
X3 = 0

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

Simplifying
X3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-8 + -1X + X2)' equal to zero and attempt to solve:

Simplifying
-8 + -1X + X2 = 0

Solving
-8 + -1X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1X + 8 + X2 = 0 + 8

Reorder the terms:
-8 + 8 + -1X + X2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1X + X2 = 0 + 8
-1X + X2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1X + X2 = 8

The X term is -1X.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1X + 0.25 + X2 = 8 + 0.25

Reorder the terms:
0.25 + -1X + X2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + -1X + X2 = 8.25

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(X + -0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
X + -0.5 = 2.872281323

Simplifying
X + -0.5 = 2.872281323

Reorder the terms:
-0.5 + X = 2.872281323

Solving
-0.5 + X = 2.872281323

Solving for variable 'X'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + X = 2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = 2.872281323 + 0.5
X = 2.872281323 + 0.5

Combine like terms: 2.872281323 + 0.5 = 3.372281323
X = 3.372281323

Simplifying
X = 3.372281323


Subproblem 2
X + -0.5 = -2.872281323

Simplifying
X + -0.5 = -2.872281323

Reorder the terms:
-0.5 + X = -2.872281323

Solving
-0.5 + X = -2.872281323

Solving for variable 'X'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + X = -2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = -2.872281323 + 0.5
X = -2.872281323 + 0.5

Combine like terms: -2.872281323 + 0.5 = -2.372281323
X = -2.372281323

Simplifying
X = -2.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.372281323, -2.372281323}
Solution
X = {3.372281323, -2.372281323}

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