0.5b^2+3b-36=0

Solution for 0.5b^2+3b-36=0 equation:

Simplifying
0.5b2 + 3b + -36 = 0

Reorder the terms:
-36 + 3b + 0.5b2 = 0

Solving
-36 + 3b + 0.5b2 = 0

Solving for variable 'b'.

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

Divide each side by '0.5'.
-72 + 6b + b2 = 0

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 6b + 72 + b2 = 0 + 72

Reorder the terms:
-72 + 72 + 6b + b2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 6b + b2 = 0 + 72
6b + b2 = 0 + 72

Combine like terms: 0 + 72 = 72
6b + b2 = 72

The b term is 6b.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6b + 9 + b2 = 72 + 9

Reorder the terms:
9 + 6b + b2 = 72 + 9

Combine like terms: 72 + 9 = 81
9 + 6b + b2 = 81

Factor a perfect square on the left side:
(b + 3)(b + 3) = 81

Calculate the square root of the right side: 9

Break this problem into two subproblems by setting 
(b + 3) equal to 9 and -9.

Subproblem 1
b + 3 = 9

Simplifying
b + 3 = 9

Reorder the terms:
3 + b = 9

Solving
3 + b = 9

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + b = 9 + -3

Combine like terms: 3 + -3 = 0
0 + b = 9 + -3
b = 9 + -3

Combine like terms: 9 + -3 = 6
b = 6

Simplifying
b = 6

Subproblem 2
b + 3 = -9

Simplifying
b + 3 = -9

Reorder the terms:
3 + b = -9

Solving
3 + b = -9

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + b = -9 + -3

Combine like terms: 3 + -3 = 0
0 + b = -9 + -3
b = -9 + -3

Combine like terms: -9 + -3 = -12
b = -12

Simplifying
b = -12

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {6, -12}