b^2-.4b-.21=0

Solution for b^2-.4b-.21=0 equation:

Simplifying
b2 + -0.4b + -0.21 = 0

Reorder the terms:
-0.21 + -0.4b + b2 = 0

Solving
-0.21 + -0.4b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '0.21' to each side of the equation.
-0.21 + -0.4b + 0.21 + b2 = 0 + 0.21

Reorder the terms:
-0.21 + 0.21 + -0.4b + b2 = 0 + 0.21

Combine like terms: -0.21 + 0.21 = 0.00
0.00 + -0.4b + b2 = 0 + 0.21
-0.4b + b2 = 0 + 0.21

Combine like terms: 0 + 0.21 = 0.21
-0.4b + b2 = 0.21

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 = 0.21 + 0.04

Reorder the terms:
0.04 + -0.4b + b2 = 0.21 + 0.04

Combine like terms: 0.21 + 0.04 = 0.25
0.04 + -0.4b + b2 = 0.25

Factor a perfect square on the left side:
(b + -0.2)(b + -0.2) = 0.25

Calculate the square root of the right side: 0.5

Break this problem into two subproblems by setting 
(b + -0.2) equal to 0.5 and -0.5.

Subproblem 1
b + -0.2 = 0.5

Simplifying
b + -0.2 = 0.5

Reorder the terms:
-0.2 + b = 0.5

Solving
-0.2 + b = 0.5

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 = 0.5 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + b = 0.5 + 0.2
b = 0.5 + 0.2

Combine like terms: 0.5 + 0.2 = 0.7
b = 0.7

Simplifying
b = 0.7

Subproblem 2
b + -0.2 = -0.5

Simplifying
b + -0.2 = -0.5

Reorder the terms:
-0.2 + b = -0.5

Solving
-0.2 + b = -0.5

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 = -0.5 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + b = -0.5 + 0.2
b = -0.5 + 0.2

Combine like terms: -0.5 + 0.2 = -0.3
b = -0.3

Simplifying
b = -0.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.7, -0.3}