2x^6-14x^7+7x^8=

Solution for 2x^6-14x^7+7x^8= equation:

Simplifying
2x6 + -14x7 + 7x8 = 0

Solving
2x6 + -14x7 + 7x8 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x6'.
x6(2 + -14x + 7x2) = 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 '(2 + -14x + 7x2)' equal to zero and attempt to solve:

Simplifying
2 + -14x + 7x2 = 0

Solving
2 + -14x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.2857142857 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -2x + -0.2857142857 + x2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -2x + x2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.2857142857
-2x + x2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-2x + x2 = -0.2857142857

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.2857142857 + 1

Reorder the terms:
1 + -2x + x2 = -0.2857142857 + 1

Combine like terms: -0.2857142857 + 1 = 0.7142857143
1 + -2x + x2 = 0.7142857143

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.7142857143

Calculate the square root of the right side: 0.845154255

Break this problem into two subproblems by setting 
(x + -1) equal to 0.845154255 and -0.845154255.

Subproblem 1
x + -1 = 0.845154255

Simplifying
x + -1 = 0.845154255

Reorder the terms:
-1 + x = 0.845154255

Solving
-1 + x = 0.845154255

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 0.845154255 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.845154255 + 1
x = 0.845154255 + 1

Combine like terms: 0.845154255 + 1 = 1.845154255
x = 1.845154255

Simplifying
x = 1.845154255

Subproblem 2
x + -1 = -0.845154255

Simplifying
x + -1 = -0.845154255

Reorder the terms:
-1 + x = -0.845154255

Solving
-1 + x = -0.845154255

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -0.845154255 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.845154255 + 1
x = -0.845154255 + 1

Combine like terms: -0.845154255 + 1 = 0.154845745
x = 0.154845745

Simplifying
x = 0.154845745

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.845154255, 0.154845745}
Solution
x = {1.845154255, 0.154845745}