50000s^2-2760s-1656=0

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Solution for 50000s^2-2760s-1656=0 equation: 


Simplifying
50000s2 + -2760s + -1656 = 0

Reorder the terms:
-1656 + -2760s + 50000s2 = 0

Solving
-1656 + -2760s + 50000s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-207 + -345s + 6250s2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-207 + -345s + 6250s2)' equal to zero and attempt to solve:

Simplifying
-207 + -345s + 6250s2 = 0

Solving
-207 + -345s + 6250s2 = 0

Begin completing the square.  Divide all terms by
6250 the coefficient of the squared term: 

Divide each side by '6250'.
-0.03312 + -0.0552s + s2 = 0.0

Move the constant term to the right:

Add '0.03312' to each side of the equation.
-0.03312 + -0.0552s + 0.03312 + s2 = 0.0 + 0.03312

Reorder the terms:
-0.03312 + 0.03312 + -0.0552s + s2 = 0.0 + 0.03312

Combine like terms: -0.03312 + 0.03312 = 0.00000
0.00000 + -0.0552s + s2 = 0.0 + 0.03312
-0.0552s + s2 = 0.0 + 0.03312

Combine like terms: 0.0 + 0.03312 = 0.03312
-0.0552s + s2 = 0.03312

The s term is -0.0552s.  Take half its coefficient (-0.0276).
Square it (0.00076176) and add it to both sides.

Add '0.00076176' to each side of the equation.
-0.0552s + 0.00076176 + s2 = 0.03312 + 0.00076176

Reorder the terms:
0.00076176 + -0.0552s + s2 = 0.03312 + 0.00076176

Combine like terms: 0.03312 + 0.00076176 = 0.03388176
0.00076176 + -0.0552s + s2 = 0.03388176

Factor a perfect square on the left side:
(s + -0.0276)(s + -0.0276) = 0.03388176

Calculate the square root of the right side: 0.184069987

Break this problem into two subproblems by setting 
(s + -0.0276) equal to 0.184069987 and -0.184069987.


Subproblem 1
s + -0.0276 = 0.184069987

Simplifying
s + -0.0276 = 0.184069987

Reorder the terms:
-0.0276 + s = 0.184069987

Solving
-0.0276 + s = 0.184069987

Solving for variable 's'.

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

Add '0.0276' to each side of the equation.
-0.0276 + 0.0276 + s = 0.184069987 + 0.0276

Combine like terms: -0.0276 + 0.0276 = 0.0000
0.0000 + s = 0.184069987 + 0.0276
s = 0.184069987 + 0.0276

Combine like terms: 0.184069987 + 0.0276 = 0.211669987
s = 0.211669987

Simplifying
s = 0.211669987


Subproblem 2
s + -0.0276 = -0.184069987

Simplifying
s + -0.0276 = -0.184069987

Reorder the terms:
-0.0276 + s = -0.184069987

Solving
-0.0276 + s = -0.184069987

Solving for variable 's'.

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

Add '0.0276' to each side of the equation.
-0.0276 + 0.0276 + s = -0.184069987 + 0.0276

Combine like terms: -0.0276 + 0.0276 = 0.0000
0.0000 + s = -0.184069987 + 0.0276
s = -0.184069987 + 0.0276

Combine like terms: -0.184069987 + 0.0276 = -0.156469987
s = -0.156469987

Simplifying
s = -0.156469987


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.211669987, -0.156469987}
Solution
s = {0.211669987, -0.156469987}

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