180=.5s^2+1.1s

Solution for 180=.5s^2+1.1s equation:

Simplifying
180 = 0.5s2 + 1.1s

Reorder the terms:
180 = 1.1s + 0.5s2

Solving
180 = 1.1s + 0.5s2

Solving for variable 's'.

Reorder the terms:
180 + -1.1s + -0.5s2 = 1.1s + -1.1s + 0.5s2 + -0.5s2

Combine like terms: 1.1s + -1.1s = 0.0
180 + -1.1s + -0.5s2 = 0.0 + 0.5s2 + -0.5s2
180 + -1.1s + -0.5s2 = 0.5s2 + -0.5s2

Combine like terms: 0.5s2 + -0.5s2 = 0.0
180 + -1.1s + -0.5s2 = 0.0

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

Divide each side by '-0.5'.
-360 + 2.2s + s2 = 0

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + 2.2s + 360 + s2 = 0 + 360

Reorder the terms:
-360 + 360 + 2.2s + s2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + 2.2s + s2 = 0 + 360
2.2s + s2 = 0 + 360

Combine like terms: 0 + 360 = 360
2.2s + s2 = 360

The s term is 2.2s.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2s + 1.21 + s2 = 360 + 1.21

Reorder the terms:
1.21 + 2.2s + s2 = 360 + 1.21

Combine like terms: 360 + 1.21 = 361.21
1.21 + 2.2s + s2 = 361.21

Factor a perfect square on the left side:
(s + 1.1)(s + 1.1) = 361.21

Calculate the square root of the right side: 19.005525512

Break this problem into two subproblems by setting 
(s + 1.1) equal to 19.005525512 and -19.005525512.

Subproblem 1
s + 1.1 = 19.005525512

Simplifying
s + 1.1 = 19.005525512

Reorder the terms:
1.1 + s = 19.005525512

Solving
1.1 + s = 19.005525512

Solving for variable 's'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + s = 19.005525512 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + s = 19.005525512 + -1.1
s = 19.005525512 + -1.1

Combine like terms: 19.005525512 + -1.1 = 17.905525512
s = 17.905525512

Simplifying
s = 17.905525512

Subproblem 2
s + 1.1 = -19.005525512

Simplifying
s + 1.1 = -19.005525512

Reorder the terms:
1.1 + s = -19.005525512

Solving
1.1 + s = -19.005525512

Solving for variable 's'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + s = -19.005525512 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + s = -19.005525512 + -1.1
s = -19.005525512 + -1.1

Combine like terms: -19.005525512 + -1.1 = -20.105525512
s = -20.105525512

Simplifying
s = -20.105525512

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {17.905525512, -20.105525512}