x^10-2x^9+x^8=0

Solution for x^10-2x^9+x^8=0 equation:

Simplifying
x10 + -2x9 + x8 = 0

Reorder the terms:
x8 + -2x9 + x10 = 0

Solving
x8 + -2x9 + x10 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x8'.
x8(1 + -2x + x2) = 0

Factor a trinomial.
x8((1 + -1x)(1 + -1x)) = 0

Subproblem 1
Set the factor 'x8' equal to zero and attempt to solve:

Simplifying
x8 = 0

Solving
x8 = 0

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

Simplifying
x8 = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {1, 1}