s^2+250s-250=0

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Solution for s^2+250s-250=0 equation: 


Simplifying
s2 + 250s + -250 = 0

Reorder the terms:
-250 + 250s + s2 = 0

Solving
-250 + 250s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + 250s + 250 + s2 = 0 + 250

Reorder the terms:
-250 + 250 + 250s + s2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + 250s + s2 = 0 + 250
250s + s2 = 0 + 250

Combine like terms: 0 + 250 = 250
250s + s2 = 250

The s term is 250s.  Take half its coefficient (125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
250s + 15625 + s2 = 250 + 15625

Reorder the terms:
15625 + 250s + s2 = 250 + 15625

Combine like terms: 250 + 15625 = 15875
15625 + 250s + s2 = 15875

Factor a perfect square on the left side:
(s + 125)(s + 125) = 15875

Calculate the square root of the right side: 125.996031684

Break this problem into two subproblems by setting 
(s + 125) equal to 125.996031684 and -125.996031684.


Subproblem 1
s + 125 = 125.996031684

Simplifying
s + 125 = 125.996031684

Reorder the terms:
125 + s = 125.996031684

Solving
125 + s = 125.996031684

Solving for variable 's'.

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

Add '-125' to each side of the equation.
125 + -125 + s = 125.996031684 + -125

Combine like terms: 125 + -125 = 0
0 + s = 125.996031684 + -125
s = 125.996031684 + -125

Combine like terms: 125.996031684 + -125 = 0.996031684
s = 0.996031684

Simplifying
s = 0.996031684


Subproblem 2
s + 125 = -125.996031684

Simplifying
s + 125 = -125.996031684

Reorder the terms:
125 + s = -125.996031684

Solving
125 + s = -125.996031684

Solving for variable 's'.

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

Add '-125' to each side of the equation.
125 + -125 + s = -125.996031684 + -125

Combine like terms: 125 + -125 = 0
0 + s = -125.996031684 + -125
s = -125.996031684 + -125

Combine like terms: -125.996031684 + -125 = -250.996031684
s = -250.996031684

Simplifying
s = -250.996031684


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.996031684, -250.996031684}

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