16s^2+72s+8=0

Solution for 16s^2+72s+8=0 equation:

Simplifying
16s2 + 72s + 8 = 0

Reorder the terms:
8 + 72s + 16s2 = 0

Solving
8 + 72s + 16s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + 9s + 2s2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + 9s + 2s2)' equal to zero and attempt to solve:

Simplifying
1 + 9s + 2s2 = 0

Solving
1 + 9s + 2s2 = 0

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

Divide each side by '2'.
0.5 + 4.5s + s2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 4.5s + -0.5 + s2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 4.5s + s2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 4.5s + s2 = 0 + -0.5
4.5s + s2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
4.5s + s2 = -0.5

The s term is 4.5s.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5s + 5.0625 + s2 = -0.5 + 5.0625

Reorder the terms:
5.0625 + 4.5s + s2 = -0.5 + 5.0625

Combine like terms: -0.5 + 5.0625 = 4.5625
5.0625 + 4.5s + s2 = 4.5625

Factor a perfect square on the left side:
(s + 2.25)(s + 2.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(s + 2.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
s + 2.25 = 2.136000936

Simplifying
s + 2.25 = 2.136000936

Reorder the terms:
2.25 + s = 2.136000936

Solving
2.25 + s = 2.136000936

Solving for variable 's'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + s = 2.136000936 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + s = 2.136000936 + -2.25
s = 2.136000936 + -2.25

Combine like terms: 2.136000936 + -2.25 = -0.113999064
s = -0.113999064

Simplifying
s = -0.113999064

Subproblem 2
s + 2.25 = -2.136000936

Simplifying
s + 2.25 = -2.136000936

Reorder the terms:
2.25 + s = -2.136000936

Solving
2.25 + s = -2.136000936

Solving for variable 's'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + s = -2.136000936 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + s = -2.136000936 + -2.25
s = -2.136000936 + -2.25

Combine like terms: -2.136000936 + -2.25 = -4.386000936
s = -4.386000936

Simplifying
s = -4.386000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.113999064, -4.386000936}
Solution
s = {-0.113999064, -4.386000936}