200=5s(100+2s)

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Solution for 200=5s(100+2s) equation: 


Simplifying
200 = 5s(100 + 2s)
200 = (100 * 5s + 2s * 5s)
200 = (500s + 10s2)

Solving
200 = 500s + 10s2

Solving for variable 's'.

Reorder the terms:
200 + -500s + -10s2 = 500s + -500s + 10s2 + -10s2

Combine like terms: 500s + -500s = 0
200 + -500s + -10s2 = 0 + 10s2 + -10s2
200 + -500s + -10s2 = 10s2 + -10s2

Combine like terms: 10s2 + -10s2 = 0
200 + -500s + -10s2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(20 + -50s + -1s2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(20 + -50s + -1s2)' equal to zero and attempt to solve:

Simplifying
20 + -50s + -1s2 = 0

Solving
20 + -50s + -1s2 = 0

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

Divide each side by '-1'.
-20 + 50s + s2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 50s + 20 + s2 = 0 + 20

Reorder the terms:
-20 + 20 + 50s + s2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 50s + s2 = 0 + 20
50s + s2 = 0 + 20

Combine like terms: 0 + 20 = 20
50s + s2 = 20

The s term is 50s.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50s + 625 + s2 = 20 + 625

Reorder the terms:
625 + 50s + s2 = 20 + 625

Combine like terms: 20 + 625 = 645
625 + 50s + s2 = 645

Factor a perfect square on the left side:
(s + 25)(s + 25) = 645

Calculate the square root of the right side: 25.396850198

Break this problem into two subproblems by setting 
(s + 25) equal to 25.396850198 and -25.396850198.


Subproblem 1
s + 25 = 25.396850198

Simplifying
s + 25 = 25.396850198

Reorder the terms:
25 + s = 25.396850198

Solving
25 + s = 25.396850198

Solving for variable 's'.

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

Add '-25' to each side of the equation.
25 + -25 + s = 25.396850198 + -25

Combine like terms: 25 + -25 = 0
0 + s = 25.396850198 + -25
s = 25.396850198 + -25

Combine like terms: 25.396850198 + -25 = 0.396850198
s = 0.396850198

Simplifying
s = 0.396850198


Subproblem 2
s + 25 = -25.396850198

Simplifying
s + 25 = -25.396850198

Reorder the terms:
25 + s = -25.396850198

Solving
25 + s = -25.396850198

Solving for variable 's'.

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

Add '-25' to each side of the equation.
25 + -25 + s = -25.396850198 + -25

Combine like terms: 25 + -25 = 0
0 + s = -25.396850198 + -25
s = -25.396850198 + -25

Combine like terms: -25.396850198 + -25 = -50.396850198
s = -50.396850198

Simplifying
s = -50.396850198


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.396850198, -50.396850198}
Solution
s = {0.396850198, -50.396850198}

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