b^2-1.185b+0.197=0

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Solution for b^2-1.185b+0.197=0 equation: 


Simplifying
b2 + -1.185b + 0.197 = 0

Reorder the terms:
0.197 + -1.185b + b2 = 0

Solving
0.197 + -1.185b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-0.197' to each side of the equation.
0.197 + -1.185b + -0.197 + b2 = 0 + -0.197

Reorder the terms:
0.197 + -0.197 + -1.185b + b2 = 0 + -0.197

Combine like terms: 0.197 + -0.197 = 0.000
0.000 + -1.185b + b2 = 0 + -0.197
-1.185b + b2 = 0 + -0.197

Combine like terms: 0 + -0.197 = -0.197
-1.185b + b2 = -0.197

The b term is -1.185b.  Take half its coefficient (-0.5925).
Square it (0.35105625) and add it to both sides.

Add '0.35105625' to each side of the equation.
-1.185b + 0.35105625 + b2 = -0.197 + 0.35105625

Reorder the terms:
0.35105625 + -1.185b + b2 = -0.197 + 0.35105625

Combine like terms: -0.197 + 0.35105625 = 0.15405625
0.35105625 + -1.185b + b2 = 0.15405625

Factor a perfect square on the left side:
(b + -0.5925)(b + -0.5925) = 0.15405625

Calculate the square root of the right side: 0.3925

Break this problem into two subproblems by setting 
(b + -0.5925) equal to 0.3925 and -0.3925.


Subproblem 1
b + -0.5925 = 0.3925

Simplifying
b + -0.5925 = 0.3925

Reorder the terms:
-0.5925 + b = 0.3925

Solving
-0.5925 + b = 0.3925

Solving for variable 'b'.

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

Add '0.5925' to each side of the equation.
-0.5925 + 0.5925 + b = 0.3925 + 0.5925

Combine like terms: -0.5925 + 0.5925 = 0.0000
0.0000 + b = 0.3925 + 0.5925
b = 0.3925 + 0.5925

Combine like terms: 0.3925 + 0.5925 = 0.985
b = 0.985

Simplifying
b = 0.985


Subproblem 2
b + -0.5925 = -0.3925

Simplifying
b + -0.5925 = -0.3925

Reorder the terms:
-0.5925 + b = -0.3925

Solving
-0.5925 + b = -0.3925

Solving for variable 'b'.

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

Add '0.5925' to each side of the equation.
-0.5925 + 0.5925 + b = -0.3925 + 0.5925

Combine like terms: -0.5925 + 0.5925 = 0.0000
0.0000 + b = -0.3925 + 0.5925
b = -0.3925 + 0.5925

Combine like terms: -0.3925 + 0.5925 = 0.2
b = 0.2

Simplifying
b = 0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.985, 0.2}

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