10b^2-20b+2=0

Solution for 10b^2-20b+2=0 equation:

Simplifying
10b2 + -20b + 2 = 0

Reorder the terms:
2 + -20b + 10b2 = 0

Solving
2 + -20b + 10b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -10b + 5b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -10b + 5b2)' equal to zero and attempt to solve:

Simplifying
1 + -10b + 5b2 = 0

Solving
1 + -10b + 5b2 = 0

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

Divide each side by '5'.
0.2 + -2b + b2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -2b + -0.2 + b2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -2b + b2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -2b + b2 = 0 + -0.2
-2b + b2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-2b + b2 = -0.2

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 = -0.2 + 1

Reorder the terms:
1 + -2b + b2 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + -2b + b2 = 0.8

Factor a perfect square on the left side:
(b + -1)(b + -1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
(b + -1) equal to 0.894427191 and -0.894427191.

Subproblem 1
b + -1 = 0.894427191

Simplifying
b + -1 = 0.894427191

Reorder the terms:
-1 + b = 0.894427191

Solving
-1 + b = 0.894427191

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 = 0.894427191 + 1

Combine like terms: -1 + 1 = 0
0 + b = 0.894427191 + 1
b = 0.894427191 + 1

Combine like terms: 0.894427191 + 1 = 1.894427191
b = 1.894427191

Simplifying
b = 1.894427191

Subproblem 2
b + -1 = -0.894427191

Simplifying
b + -1 = -0.894427191

Reorder the terms:
-1 + b = -0.894427191

Solving
-1 + b = -0.894427191

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 = -0.894427191 + 1

Combine like terms: -1 + 1 = 0
0 + b = -0.894427191 + 1
b = -0.894427191 + 1

Combine like terms: -0.894427191 + 1 = 0.105572809
b = 0.105572809

Simplifying
b = 0.105572809

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.894427191, 0.105572809}
Solution
b = {1.894427191, 0.105572809}