s^2+0.2s-0.08=0

Solution for s^2+0.2s-0.08=0 equation:

Simplifying
s2 + 0.2s + -0.08 = 0

Reorder the terms:
-0.08 + 0.2s + s2 = 0

Solving
-0.08 + 0.2s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '0.08' to each side of the equation.
-0.08 + 0.2s + 0.08 + s2 = 0 + 0.08

Reorder the terms:
-0.08 + 0.08 + 0.2s + s2 = 0 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + 0.2s + s2 = 0 + 0.08
0.2s + s2 = 0 + 0.08

Combine like terms: 0 + 0.08 = 0.08
0.2s + s2 = 0.08

The s term is 0.2s.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2s + 0.01 + s2 = 0.08 + 0.01

Reorder the terms:
0.01 + 0.2s + s2 = 0.08 + 0.01

Combine like terms: 0.08 + 0.01 = 0.09
0.01 + 0.2s + s2 = 0.09

Factor a perfect square on the left side:
(s + 0.1)(s + 0.1) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(s + 0.1) equal to 0.3 and -0.3.

Subproblem 1
s + 0.1 = 0.3

Simplifying
s + 0.1 = 0.3

Reorder the terms:
0.1 + s = 0.3

Solving
0.1 + s = 0.3

Solving for variable 's'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + s = 0.3 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + s = 0.3 + -0.1
s = 0.3 + -0.1

Combine like terms: 0.3 + -0.1 = 0.2
s = 0.2

Simplifying
s = 0.2

Subproblem 2
s + 0.1 = -0.3

Simplifying
s + 0.1 = -0.3

Reorder the terms:
0.1 + s = -0.3

Solving
0.1 + s = -0.3

Solving for variable 's'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + s = -0.3 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + s = -0.3 + -0.1
s = -0.3 + -0.1

Combine like terms: -0.3 + -0.1 = -0.4
s = -0.4

Simplifying
s = -0.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.2, -0.4}