4x^5-44x^4+4x^3=0

Solution for 4x^5-44x^4+4x^3=0 equation:

Simplifying
4x5 + -44x4 + 4x3 = 0

Reorder the terms:
4x3 + -44x4 + 4x5 = 0

Solving
4x3 + -44x4 + 4x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x3'.
4x3(1 + -11x + x2) = 0

Ignore the factor 4.
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 '(1 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -11x + x2 = 0

Solving
1 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -11x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -11x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -11x + x2 = 0 + -1
-11x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-11x + x2 = -1

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -1 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -1 + 30.25

Combine like terms: -1 + 30.25 = 29.25
30.25 + -11x + x2 = 29.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
x + -5.5 = 5.408326913

Simplifying
x + -5.5 = 5.408326913

Reorder the terms:
-5.5 + x = 5.408326913

Solving
-5.5 + x = 5.408326913

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.408326913 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.408326913 + 5.5
x = 5.408326913 + 5.5

Combine like terms: 5.408326913 + 5.5 = 10.908326913
x = 10.908326913

Simplifying
x = 10.908326913

Subproblem 2
x + -5.5 = -5.408326913

Simplifying
x + -5.5 = -5.408326913

Reorder the terms:
-5.5 + x = -5.408326913

Solving
-5.5 + x = -5.408326913

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.408326913 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.408326913 + 5.5
x = -5.408326913 + 5.5

Combine like terms: -5.408326913 + 5.5 = 0.091673087
x = 0.091673087

Simplifying
x = 0.091673087

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.908326913, 0.091673087}
Solution
x = {10.908326913, 0.091673087}