x^5-20x^4-36x^3=

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Solution for x^5-20x^4-36x^3= equation: 


Simplifying
x5 + -20x4 + -36x3 = 0

Reorder the terms:
-36x3 + -20x4 + x5 = 0

Solving
-36x3 + -20x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-36 + -20x + 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 '(-36 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + -20x + x2 = 0

Solving
-36 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -20x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -20x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -20x + x2 = 0 + 36
-20x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-20x + x2 = 36

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 36 + 100

Reorder the terms:
100 + -20x + x2 = 36 + 100

Combine like terms: 36 + 100 = 136
100 + -20x + x2 = 136

Factor a perfect square on the left side:
(x + -10)(x + -10) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + -10) equal to 11.66190379 and -11.66190379.


Subproblem 1
x + -10 = 11.66190379

Simplifying
x + -10 = 11.66190379

Reorder the terms:
-10 + x = 11.66190379

Solving
-10 + x = 11.66190379

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 11.66190379 + 10

Combine like terms: -10 + 10 = 0
0 + x = 11.66190379 + 10
x = 11.66190379 + 10

Combine like terms: 11.66190379 + 10 = 21.66190379
x = 21.66190379

Simplifying
x = 21.66190379


Subproblem 2
x + -10 = -11.66190379

Simplifying
x + -10 = -11.66190379

Reorder the terms:
-10 + x = -11.66190379

Solving
-10 + x = -11.66190379

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -11.66190379 + 10

Combine like terms: -10 + 10 = 0
0 + x = -11.66190379 + 10
x = -11.66190379 + 10

Combine like terms: -11.66190379 + 10 = -1.66190379
x = -1.66190379

Simplifying
x = -1.66190379


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.66190379, -1.66190379}
Solution
x = {21.66190379, -1.66190379}

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