y^5-14y^4+31y^3=0

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Solution for y^5-14y^4+31y^3=0 equation: 


Simplifying
y5 + -14y4 + 31y3 = 0

Reorder the terms:
31y3 + -14y4 + y5 = 0

Solving
31y3 + -14y4 + y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y3'.
y3(31 + -14y + y2) = 0


Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 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 '(31 + -14y + y2)' equal to zero and attempt to solve:

Simplifying
31 + -14y + y2 = 0

Solving
31 + -14y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -14y + -31 + y2 = 0 + -31

Reorder the terms:
31 + -31 + -14y + y2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -14y + y2 = 0 + -31
-14y + y2 = 0 + -31

Combine like terms: 0 + -31 = -31
-14y + y2 = -31

The y term is -14y.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14y + 49 + y2 = -31 + 49

Reorder the terms:
49 + -14y + y2 = -31 + 49

Combine like terms: -31 + 49 = 18
49 + -14y + y2 = 18

Factor a perfect square on the left side:
(y + -7)(y + -7) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(y + -7) equal to 4.242640687 and -4.242640687.


Subproblem 1
y + -7 = 4.242640687

Simplifying
y + -7 = 4.242640687

Reorder the terms:
-7 + y = 4.242640687

Solving
-7 + y = 4.242640687

Solving for variable 'y'.

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

Add '7' to each side of the equation.
-7 + 7 + y = 4.242640687 + 7

Combine like terms: -7 + 7 = 0
0 + y = 4.242640687 + 7
y = 4.242640687 + 7

Combine like terms: 4.242640687 + 7 = 11.242640687
y = 11.242640687

Simplifying
y = 11.242640687


Subproblem 2
y + -7 = -4.242640687

Simplifying
y + -7 = -4.242640687

Reorder the terms:
-7 + y = -4.242640687

Solving
-7 + y = -4.242640687

Solving for variable 'y'.

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

Add '7' to each side of the equation.
-7 + 7 + y = -4.242640687 + 7

Combine like terms: -7 + 7 = 0
0 + y = -4.242640687 + 7
y = -4.242640687 + 7

Combine like terms: -4.242640687 + 7 = 2.757359313
y = 2.757359313

Simplifying
y = 2.757359313


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.242640687, 2.757359313}
Solution
y = {11.242640687, 2.757359313}

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