7b^2+-14b+1=0

Solution for 7b^2+-14b+1=0 equation:

Simplifying
7b2 + -14b + 1 = 0

Reorder the terms:
1 + -14b + 7b2 = 0

Solving
1 + -14b + 7b2 = 0

Solving for variable 'b'.

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

Divide each side by '7'.
0.1428571429 + -2b + b2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -2b + -0.1428571429 + b2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -2b + b2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -2b + b2 = 0 + -0.1428571429
-2b + b2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-2b + b2 = -0.1428571429

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

Add '1' to each side of the equation.
-2b + 1 + b2 = -0.1428571429 + 1

Reorder the terms:
1 + -2b + b2 = -0.1428571429 + 1

Combine like terms: -0.1428571429 + 1 = 0.8571428571
1 + -2b + b2 = 0.8571428571

Factor a perfect square on the left side:
(b + -1)(b + -1) = 0.8571428571

Calculate the square root of the right side: 0.9258201

Break this problem into two subproblems by setting 
(b + -1) equal to 0.9258201 and -0.9258201.

Subproblem 1
b + -1 = 0.9258201

Simplifying
b + -1 = 0.9258201

Reorder the terms:
-1 + b = 0.9258201

Solving
-1 + b = 0.9258201

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + b = 0.9258201 + 1

Combine like terms: -1 + 1 = 0
0 + b = 0.9258201 + 1
b = 0.9258201 + 1

Combine like terms: 0.9258201 + 1 = 1.9258201
b = 1.9258201

Simplifying
b = 1.9258201

Subproblem 2
b + -1 = -0.9258201

Simplifying
b + -1 = -0.9258201

Reorder the terms:
-1 + b = -0.9258201

Solving
-1 + b = -0.9258201

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + b = -0.9258201 + 1

Combine like terms: -1 + 1 = 0
0 + b = -0.9258201 + 1
b = -0.9258201 + 1

Combine like terms: -0.9258201 + 1 = 0.0741799
b = 0.0741799

Simplifying
b = 0.0741799

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.9258201, 0.0741799}