2b^2+24b+144=729

Solution for 2b^2+24b+144=729 equation:

Simplifying
2b2 + 24b + 144 = 729

Reorder the terms:
144 + 24b + 2b2 = 729

Solving
144 + 24b + 2b2 = 729

Solving for variable 'b'.

Reorder the terms:
144 + -729 + 24b + 2b2 = 729 + -729

Combine like terms: 144 + -729 = -585
-585 + 24b + 2b2 = 729 + -729

Combine like terms: 729 + -729 = 0
-585 + 24b + 2b2 = 0

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

Divide each side by '2'.
-292.5 + 12b + b2 = 0

Move the constant term to the right:

Add '292.5' to each side of the equation.
-292.5 + 12b + 292.5 + b2 = 0 + 292.5

Reorder the terms:
-292.5 + 292.5 + 12b + b2 = 0 + 292.5

Combine like terms: -292.5 + 292.5 = 0.0
0.0 + 12b + b2 = 0 + 292.5
12b + b2 = 0 + 292.5

Combine like terms: 0 + 292.5 = 292.5
12b + b2 = 292.5

The b term is 12b.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12b + 36 + b2 = 292.5 + 36

Reorder the terms:
36 + 12b + b2 = 292.5 + 36

Combine like terms: 292.5 + 36 = 328.5
36 + 12b + b2 = 328.5

Factor a perfect square on the left side:
(b + 6)(b + 6) = 328.5

Calculate the square root of the right side: 18.12456896

Break this problem into two subproblems by setting 
(b + 6) equal to 18.12456896 and -18.12456896.

Subproblem 1
b + 6 = 18.12456896

Simplifying
b + 6 = 18.12456896

Reorder the terms:
6 + b = 18.12456896

Solving
6 + b = 18.12456896

Solving for variable 'b'.

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

Add '-6' to each side of the equation.
6 + -6 + b = 18.12456896 + -6

Combine like terms: 6 + -6 = 0
0 + b = 18.12456896 + -6
b = 18.12456896 + -6

Combine like terms: 18.12456896 + -6 = 12.12456896
b = 12.12456896

Simplifying
b = 12.12456896

Subproblem 2
b + 6 = -18.12456896

Simplifying
b + 6 = -18.12456896

Reorder the terms:
6 + b = -18.12456896

Solving
6 + b = -18.12456896

Solving for variable 'b'.

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

Add '-6' to each side of the equation.
6 + -6 + b = -18.12456896 + -6

Combine like terms: 6 + -6 = 0
0 + b = -18.12456896 + -6
b = -18.12456896 + -6

Combine like terms: -18.12456896 + -6 = -24.12456896
b = -24.12456896

Simplifying
b = -24.12456896

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {12.12456896, -24.12456896}