3s+s(1-s)=s-17

Solution for 3s+s(1-s)=s-17 equation:

Simplifying
3s + s(1 + -1s) = s + -17
3s + (1 * s + -1s * s) = s + -17
3s + (1s + -1s2) = s + -17

Combine like terms: 3s + 1s = 4s
4s + -1s2 = s + -17

Reorder the terms:
4s + -1s2 = -17 + s

Solving
4s + -1s2 = -17 + s

Solving for variable 's'.

Reorder the terms:
17 + 4s + -1s + -1s2 = -17 + s + 17 + -1s

Combine like terms: 4s + -1s = 3s
17 + 3s + -1s2 = -17 + s + 17 + -1s

Reorder the terms:
17 + 3s + -1s2 = -17 + 17 + s + -1s

Combine like terms: -17 + 17 = 0
17 + 3s + -1s2 = 0 + s + -1s
17 + 3s + -1s2 = s + -1s

Combine like terms: s + -1s = 0
17 + 3s + -1s2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + -3s + s2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -3s + 17 + s2 = 0 + 17

Reorder the terms:
-17 + 17 + -3s + s2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3s + s2 = 0 + 17
-3s + s2 = 0 + 17

Combine like terms: 0 + 17 = 17
-3s + s2 = 17

The s term is -3s.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3s + 2.25 + s2 = 17 + 2.25

Reorder the terms:
2.25 + -3s + s2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + -3s + s2 = 19.25

Factor a perfect square on the left side:
(s + -1.5)(s + -1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(s + -1.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
s + -1.5 = 4.387482194

Simplifying
s + -1.5 = 4.387482194

Reorder the terms:
-1.5 + s = 4.387482194

Solving
-1.5 + s = 4.387482194

Solving for variable 's'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = 4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = 4.387482194 + 1.5
s = 4.387482194 + 1.5

Combine like terms: 4.387482194 + 1.5 = 5.887482194
s = 5.887482194

Simplifying
s = 5.887482194

Subproblem 2
s + -1.5 = -4.387482194

Simplifying
s + -1.5 = -4.387482194

Reorder the terms:
-1.5 + s = -4.387482194

Solving
-1.5 + s = -4.387482194

Solving for variable 's'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = -4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = -4.387482194 + 1.5
s = -4.387482194 + 1.5

Combine like terms: -4.387482194 + 1.5 = -2.887482194
s = -2.887482194

Simplifying
s = -2.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {5.887482194, -2.887482194}