-5b^2+b+1=0

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

Simplifying
-5b2 + b + 1 = 0

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

Solving
1 + b + -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 + -0.2b + b2 = 0

Move the constant term to the right:

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

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

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

Combine like terms: 0 + 0.2 = 0.2
-0.2b + 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.
-0.2b + 0.25 + b2 = 0.2 + 0.25

Reorder the terms:
0.25 + -0.2b + b2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
0.25 + -0.2b + b2 = 0.45

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(b + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
b + 0.5 = 0.670820393

Simplifying
b + 0.5 = 0.670820393

Reorder the terms:
0.5 + b = 0.670820393

Solving
0.5 + b = 0.670820393

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 = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 0.670820393 + -0.5
b = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
b = 0.170820393

Simplifying
b = 0.170820393

Subproblem 2
b + 0.5 = -0.670820393

Simplifying
b + 0.5 = -0.670820393

Reorder the terms:
0.5 + b = -0.670820393

Solving
0.5 + b = -0.670820393

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 = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -0.670820393 + -0.5
b = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
b = -1.170820393

Simplifying
b = -1.170820393

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.170820393, -1.170820393}