s^2-185s-1717=0

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Solution for s^2-185s-1717=0 equation: 


Simplifying
s2 + -185s + -1717 = 0

Reorder the terms:
-1717 + -185s + s2 = 0

Solving
-1717 + -185s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '1717' to each side of the equation.
-1717 + -185s + 1717 + s2 = 0 + 1717

Reorder the terms:
-1717 + 1717 + -185s + s2 = 0 + 1717

Combine like terms: -1717 + 1717 = 0
0 + -185s + s2 = 0 + 1717
-185s + s2 = 0 + 1717

Combine like terms: 0 + 1717 = 1717
-185s + s2 = 1717

The s term is -185s.  Take half its coefficient (-92.5).
Square it (8556.25) and add it to both sides.

Add '8556.25' to each side of the equation.
-185s + 8556.25 + s2 = 1717 + 8556.25

Reorder the terms:
8556.25 + -185s + s2 = 1717 + 8556.25

Combine like terms: 1717 + 8556.25 = 10273.25
8556.25 + -185s + s2 = 10273.25

Factor a perfect square on the left side:
(s + -92.5)(s + -92.5) = 10273.25

Calculate the square root of the right side: 101.357042183

Break this problem into two subproblems by setting 
(s + -92.5) equal to 101.357042183 and -101.357042183.


Subproblem 1
s + -92.5 = 101.357042183

Simplifying
s + -92.5 = 101.357042183

Reorder the terms:
-92.5 + s = 101.357042183

Solving
-92.5 + s = 101.357042183

Solving for variable 's'.

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

Add '92.5' to each side of the equation.
-92.5 + 92.5 + s = 101.357042183 + 92.5

Combine like terms: -92.5 + 92.5 = 0.0
0.0 + s = 101.357042183 + 92.5
s = 101.357042183 + 92.5

Combine like terms: 101.357042183 + 92.5 = 193.857042183
s = 193.857042183

Simplifying
s = 193.857042183


Subproblem 2
s + -92.5 = -101.357042183

Simplifying
s + -92.5 = -101.357042183

Reorder the terms:
-92.5 + s = -101.357042183

Solving
-92.5 + s = -101.357042183

Solving for variable 's'.

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

Add '92.5' to each side of the equation.
-92.5 + 92.5 + s = -101.357042183 + 92.5

Combine like terms: -92.5 + 92.5 = 0.0
0.0 + s = -101.357042183 + 92.5
s = -101.357042183 + 92.5

Combine like terms: -101.357042183 + 92.5 = -8.857042183
s = -8.857042183

Simplifying
s = -8.857042183


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {193.857042183, -8.857042183}

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