x^8-5x^7-3x^6=

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Solution for x^8-5x^7-3x^6= equation: 


Simplifying
x8 + -5x7 + -3x6 = 0

Reorder the terms:
-3x6 + -5x7 + x8 = 0

Solving
-3x6 + -5x7 + x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x6'.
x6(-3 + -5x + x2) = 0


Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve:

Simplifying
x6 = 0

Solving
x6 = 0

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

Simplifying
x6 = 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 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -5x + x2 = 0

Solving
-3 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x + x2 = 0 + 3
-5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5x + x2 = 3

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 3 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5x + x2 = 9.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
x + -2.5 = 3.041381265

Simplifying
x + -2.5 = 3.041381265

Reorder the terms:
-2.5 + x = 3.041381265

Solving
-2.5 + x = 3.041381265

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.041381265 + 2.5
x = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
x = 5.541381265

Simplifying
x = 5.541381265


Subproblem 2
x + -2.5 = -3.041381265

Simplifying
x + -2.5 = -3.041381265

Reorder the terms:
-2.5 + x = -3.041381265

Solving
-2.5 + x = -3.041381265

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.041381265 + 2.5
x = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
x = -0.541381265

Simplifying
x = -0.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.541381265, -0.541381265}
Solution
x = {5.541381265, -0.541381265}

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