12.5b^2+5b+.5=0

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Solution for 12.5b^2+5b+.5=0 equation:


Simplifying
12.5b2 + 5b + 0.5 = 0

Reorder the terms:
0.5 + 5b + 12.5b2 = 0

Solving
0.5 + 5b + 12.5b2 = 0

Solving for variable 'b'.

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

Divide each side by '12.5'.
0.04 + 0.4b + b2 = 0

Move the constant term to the right:

Add '-0.04' to each side of the equation.
0.04 + 0.4b + -0.04 + b2 = 0 + -0.04

Reorder the terms:
0.04 + -0.04 + 0.4b + b2 = 0 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
0.00 + 0.4b + b2 = 0 + -0.04
0.4b + b2 = 0 + -0.04

Combine like terms: 0 + -0.04 = -0.04
0.4b + b2 = -0.04

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 = -0.04 + 0.04

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

Combine like terms: -0.04 + 0.04 = 0.00
0.04 + 0.4b + b2 = 0.00

Factor a perfect square on the left side:
(b + 0.2)(b + 0.2) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(b + 0.2) equal to 0.00 and 0.00.

Subproblem 1

b + 0.2 = 0.00 Simplifying b + 0.2 = 0.00 Reorder the terms: 0.2 + b = 0.00 Solving 0.2 + b = 0.00 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 = 0.00 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + b = 0.00 + -0.2 b = 0.00 + -0.2 Combine like terms: 0.00 + -0.2 = -0.2 b = -0.2 Simplifying b = -0.2

Subproblem 2

b + 0.2 = 0.00 Simplifying b + 0.2 = 0.00 Reorder the terms: 0.2 + b = 0.00 Solving 0.2 + b = 0.00 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 = 0.00 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + b = 0.00 + -0.2 b = 0.00 + -0.2 Combine like terms: 0.00 + -0.2 = -0.2 b = -0.2 Simplifying b = -0.2

Solution

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

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