7x^2-18x+1=0

Solution for 7x^2-18x+1=0 equation:

Simplifying
7x2 + -18x + 1 = 0

Reorder the terms:
1 + -18x + 7x2 = 0

Solving
1 + -18x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.1428571429 + -2.571428571x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -2.571428571x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -2.571428571x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -2.571428571x + x2 = 0 + -0.1428571429
-2.571428571x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-2.571428571x + x2 = -0.1428571429

The x term is -2.571428571x.  Take half its coefficient (-1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
-2.571428571x + 1.653061225 + x2 = -0.1428571429 + 1.653061225

Reorder the terms:
1.653061225 + -2.571428571x + x2 = -0.1428571429 + 1.653061225

Combine like terms: -0.1428571429 + 1.653061225 = 1.5102040821
1.653061225 + -2.571428571x + x2 = 1.5102040821

Factor a perfect square on the left side:
(x + -1.285714286)(x + -1.285714286) = 1.5102040821

Calculate the square root of the right side: 1.22890361

Break this problem into two subproblems by setting 
(x + -1.285714286) equal to 1.22890361 and -1.22890361.

Subproblem 1
x + -1.285714286 = 1.22890361

Simplifying
x + -1.285714286 = 1.22890361

Reorder the terms:
-1.285714286 + x = 1.22890361

Solving
-1.285714286 + x = 1.22890361

Solving for variable 'x'.

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

Add '1.285714286' to each side of the equation.
-1.285714286 + 1.285714286 + x = 1.22890361 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + x = 1.22890361 + 1.285714286
x = 1.22890361 + 1.285714286

Combine like terms: 1.22890361 + 1.285714286 = 2.514617896
x = 2.514617896

Simplifying
x = 2.514617896

Subproblem 2
x + -1.285714286 = -1.22890361

Simplifying
x + -1.285714286 = -1.22890361

Reorder the terms:
-1.285714286 + x = -1.22890361

Solving
-1.285714286 + x = -1.22890361

Solving for variable 'x'.

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

Add '1.285714286' to each side of the equation.
-1.285714286 + 1.285714286 + x = -1.22890361 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + x = -1.22890361 + 1.285714286
x = -1.22890361 + 1.285714286

Combine like terms: -1.22890361 + 1.285714286 = 0.056810676
x = 0.056810676

Simplifying
x = 0.056810676

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.514617896, 0.056810676}