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

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


Simplifying
X5 + -1X4 + -3X3 = 0

Reorder the terms:
-3X3 + -1X4 + X5 = 0

Solving
-3X3 + -1X4 + X5 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), 'X3'.
X3(-3 + -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 '(-3 + -1X + X2)' equal to zero and attempt to solve:

Simplifying
-3 + -1X + X2 = 0

Solving
-3 + -1X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1X + 3 + X2 = 0 + 3

Reorder the terms:
-3 + 3 + -1X + X2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X + X2 = 0 + 3
-1X + X2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1X + X2 = 3

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 = 3 + 0.25

Reorder the terms:
0.25 + -1X + X2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1X + X2 = 3.25

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(X + -0.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
X + -0.5 = 1.802775638

Simplifying
X + -0.5 = 1.802775638

Reorder the terms:
-0.5 + X = 1.802775638

Solving
-0.5 + X = 1.802775638

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 = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = 1.802775638 + 0.5
X = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
X = 2.302775638

Simplifying
X = 2.302775638


Subproblem 2
X + -0.5 = -1.802775638

Simplifying
X + -0.5 = -1.802775638

Reorder the terms:
-0.5 + X = -1.802775638

Solving
-0.5 + X = -1.802775638

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 = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = -1.802775638 + 0.5
X = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
X = -1.302775638

Simplifying
X = -1.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.302775638, -1.302775638}
Solution
X = {2.302775638, -1.302775638}

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