2b^2+3b+11-7b^2-5b+1=0

Solution for 2b^2+3b+11-7b^2-5b+1=0 equation:

Simplifying
2b2 + 3b + 11 + -7b2 + -5b + 1 = 0

Reorder the terms:
11 + 1 + 3b + -5b + 2b2 + -7b2 = 0

Combine like terms: 11 + 1 = 12
12 + 3b + -5b + 2b2 + -7b2 = 0

Combine like terms: 3b + -5b = -2b
12 + -2b + 2b2 + -7b2 = 0

Combine like terms: 2b2 + -7b2 = -5b2
12 + -2b + -5b2 = 0

Solving
12 + -2b + -5b2 = 0

Solving for variable 'b'.

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

Divide each side by '-5'.
-2.4 + 0.4b + b2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 0.4b + 2.4 + b2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 0.4b + b2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 0.4b + b2 = 0 + 2.4
0.4b + b2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
0.4b + b2 = 2.4

The b term is 0.4b.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4b + 0.04 + b2 = 2.4 + 0.04

Reorder the terms:
0.04 + 0.4b + b2 = 2.4 + 0.04

Combine like terms: 2.4 + 0.04 = 2.44
0.04 + 0.4b + b2 = 2.44

Factor a perfect square on the left side:
(b + 0.2)(b + 0.2) = 2.44

Calculate the square root of the right side: 1.562049935

Break this problem into two subproblems by setting 
(b + 0.2) equal to 1.562049935 and -1.562049935.

Subproblem 1
b + 0.2 = 1.562049935

Simplifying
b + 0.2 = 1.562049935

Reorder the terms:
0.2 + b = 1.562049935

Solving
0.2 + b = 1.562049935

Solving for variable 'b'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + b = 1.562049935 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + b = 1.562049935 + -0.2
b = 1.562049935 + -0.2

Combine like terms: 1.562049935 + -0.2 = 1.362049935
b = 1.362049935

Simplifying
b = 1.362049935

Subproblem 2
b + 0.2 = -1.562049935

Simplifying
b + 0.2 = -1.562049935

Reorder the terms:
0.2 + b = -1.562049935

Solving
0.2 + b = -1.562049935

Solving for variable 'b'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + b = -1.562049935 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + b = -1.562049935 + -0.2
b = -1.562049935 + -0.2

Combine like terms: -1.562049935 + -0.2 = -1.762049935
b = -1.762049935

Simplifying
b = -1.762049935

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.362049935, -1.762049935}