125=0.05s^2+1.1s

Solution for 125=0.05s^2+1.1s equation:

Simplifying
125 = 0.05s2 + 1.1s

Reorder the terms:
125 = 1.1s + 0.05s2

Solving
125 = 1.1s + 0.05s2

Solving for variable 's'.

Reorder the terms:
125 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2

Combine like terms: 1.1s + -1.1s = 0.0
125 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2
125 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2

Combine like terms: 0.05s2 + -0.05s2 = 0.00
125 + -1.1s + -0.05s2 = 0.00

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
-2500 + 22s + s2 = 0

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + 22s + 2500 + s2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + 22s + s2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + 22s + s2 = 0 + 2500
22s + s2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
22s + s2 = 2500

The s term is 22s.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22s + 121 + s2 = 2500 + 121

Reorder the terms:
121 + 22s + s2 = 2500 + 121

Combine like terms: 2500 + 121 = 2621
121 + 22s + s2 = 2621

Factor a perfect square on the left side:
(s + 11)(s + 11) = 2621

Calculate the square root of the right side: 51.195702945

Break this problem into two subproblems by setting 
(s + 11) equal to 51.195702945 and -51.195702945.

Subproblem 1
s + 11 = 51.195702945

Simplifying
s + 11 = 51.195702945

Reorder the terms:
11 + s = 51.195702945

Solving
11 + s = 51.195702945

Solving for variable 's'.

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

Add '-11' to each side of the equation.
11 + -11 + s = 51.195702945 + -11

Combine like terms: 11 + -11 = 0
0 + s = 51.195702945 + -11
s = 51.195702945 + -11

Combine like terms: 51.195702945 + -11 = 40.195702945
s = 40.195702945

Simplifying
s = 40.195702945

Subproblem 2
s + 11 = -51.195702945

Simplifying
s + 11 = -51.195702945

Reorder the terms:
11 + s = -51.195702945

Solving
11 + s = -51.195702945

Solving for variable 's'.

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

Add '-11' to each side of the equation.
11 + -11 + s = -51.195702945 + -11

Combine like terms: 11 + -11 = 0
0 + s = -51.195702945 + -11
s = -51.195702945 + -11

Combine like terms: -51.195702945 + -11 = -62.195702945
s = -62.195702945

Simplifying
s = -62.195702945

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {40.195702945, -62.195702945}