20b^2-20b+1=0

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Solution for 20b^2-20b+1=0 equation:


Simplifying
20b2 + -20b + 1 = 0

Reorder the terms:
1 + -20b + 20b2 = 0

Solving
1 + -20b + 20b2 = 0

Solving for variable 'b'.

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

Divide each side by '20'.
0.05 + -1b + b2 = 0

Move the constant term to the right:

Add '-0.05' to each side of the equation.
0.05 + -1b + -0.05 + b2 = 0 + -0.05

Reorder the terms:
0.05 + -0.05 + -1b + b2 = 0 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + -1b + b2 = 0 + -0.05
-1b + b2 = 0 + -0.05

Combine like terms: 0 + -0.05 = -0.05
-1b + b2 = -0.05

The b term is -1b.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1b + 0.25 + b2 = -0.05 + 0.25

Reorder the terms:
0.25 + -1b + b2 = -0.05 + 0.25

Combine like terms: -0.05 + 0.25 = 0.2
0.25 + -1b + b2 = 0.2

Factor a perfect square on the left side:
(b + -0.5)(b + -0.5) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(b + -0.5) equal to 0.447213596 and -0.447213596.

Subproblem 1

b + -0.5 = 0.447213596 Simplifying b + -0.5 = 0.447213596 Reorder the terms: -0.5 + b = 0.447213596 Solving -0.5 + b = 0.447213596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 0.447213596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 0.447213596 + 0.5 b = 0.447213596 + 0.5 Combine like terms: 0.447213596 + 0.5 = 0.947213596 b = 0.947213596 Simplifying b = 0.947213596

Subproblem 2

b + -0.5 = -0.447213596 Simplifying b + -0.5 = -0.447213596 Reorder the terms: -0.5 + b = -0.447213596 Solving -0.5 + b = -0.447213596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -0.447213596 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -0.447213596 + 0.5 b = -0.447213596 + 0.5 Combine like terms: -0.447213596 + 0.5 = 0.052786404 b = 0.052786404 Simplifying b = 0.052786404

Solution

The solution to the problem is based on the solutions from the subproblems. b = {0.947213596, 0.052786404}

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