5b^2+5b+1=0

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Solution for 5b^2+5b+1=0 equation:


Simplifying
5b2 + 5b + 1 = 0

Reorder the terms:
1 + 5b + 5b2 = 0

Solving
1 + 5b + 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'.
0.2 + b + b2 = 0

Move the constant term to the right:

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

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

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

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

The b term is b.  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.
 + 0.25 + b2 = -0.2 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + b2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
1.25 + b2 = 0.05

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1

b + 0.5 = 0.223606798 Simplifying b + 0.5 = 0.223606798 Reorder the terms: 0.5 + b = 0.223606798 Solving 0.5 + b = 0.223606798 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 = 0.223606798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = 0.223606798 + -0.5 b = 0.223606798 + -0.5 Combine like terms: 0.223606798 + -0.5 = -0.276393202 b = -0.276393202 Simplifying b = -0.276393202

Subproblem 2

b + 0.5 = -0.223606798 Simplifying b + 0.5 = -0.223606798 Reorder the terms: 0.5 + b = -0.223606798 Solving 0.5 + b = -0.223606798 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 = -0.223606798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + b = -0.223606798 + -0.5 b = -0.223606798 + -0.5 Combine like terms: -0.223606798 + -0.5 = -0.723606798 b = -0.723606798 Simplifying b = -0.723606798

Solution

The solution to the problem is based on the solutions from the subproblems. b = {-0.276393202, -0.723606798}

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