120=.05s^2+1.1s

Solution for 120=.05s^2+1.1s equation:

Simplifying
120 = 0.05s2 + 1.1s

Reorder the terms:
120 = 1.1s + 0.05s2

Solving
120 = 1.1s + 0.05s2

Solving for variable 's'.

Reorder the terms:
120 + -1.1s + -0.05s2 = 1.1s + -1.1s + 0.05s2 + -0.05s2

Combine like terms: 1.1s + -1.1s = 0.0
120 + -1.1s + -0.05s2 = 0.0 + 0.05s2 + -0.05s2
120 + -1.1s + -0.05s2 = 0.05s2 + -0.05s2

Combine like terms: 0.05s2 + -0.05s2 = 0.00
120 + -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'.
-2400 + 22s + s2 = 0

Move the constant term to the right:

Add '2400' to each side of the equation.
-2400 + 22s + 2400 + s2 = 0 + 2400

Reorder the terms:
-2400 + 2400 + 22s + s2 = 0 + 2400

Combine like terms: -2400 + 2400 = 0
0 + 22s + s2 = 0 + 2400
22s + s2 = 0 + 2400

Combine like terms: 0 + 2400 = 2400
22s + s2 = 2400

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 = 2400 + 121

Reorder the terms:
121 + 22s + s2 = 2400 + 121

Combine like terms: 2400 + 121 = 2521
121 + 22s + s2 = 2521

Factor a perfect square on the left side:
(s + 11)(s + 11) = 2521

Calculate the square root of the right side: 50.209560843

Break this problem into two subproblems by setting 
(s + 11) equal to 50.209560843 and -50.209560843.

Subproblem 1
s + 11 = 50.209560843

Simplifying
s + 11 = 50.209560843

Reorder the terms:
11 + s = 50.209560843

Solving
11 + s = 50.209560843

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 = 50.209560843 + -11

Combine like terms: 11 + -11 = 0
0 + s = 50.209560843 + -11
s = 50.209560843 + -11

Combine like terms: 50.209560843 + -11 = 39.209560843
s = 39.209560843

Simplifying
s = 39.209560843

Subproblem 2
s + 11 = -50.209560843

Simplifying
s + 11 = -50.209560843

Reorder the terms:
11 + s = -50.209560843

Solving
11 + s = -50.209560843

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 = -50.209560843 + -11

Combine like terms: 11 + -11 = 0
0 + s = -50.209560843 + -11
s = -50.209560843 + -11

Combine like terms: -50.209560843 + -11 = -61.209560843
s = -61.209560843

Simplifying
s = -61.209560843

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {39.209560843, -61.209560843}