s^2+11s-35=0

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Solution for s^2+11s-35=0 equation: 


Simplifying
s2 + 11s + -35 = 0

Reorder the terms:
-35 + 11s + s2 = 0

Solving
-35 + 11s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 11s + 35 + s2 = 0 + 35

Reorder the terms:
-35 + 35 + 11s + s2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 11s + s2 = 0 + 35
11s + s2 = 0 + 35

Combine like terms: 0 + 35 = 35
11s + s2 = 35

The s term is 11s.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11s + 30.25 + s2 = 35 + 30.25

Reorder the terms:
30.25 + 11s + s2 = 35 + 30.25

Combine like terms: 35 + 30.25 = 65.25
30.25 + 11s + s2 = 65.25

Factor a perfect square on the left side:
(s + 5.5)(s + 5.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(s + 5.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
s + 5.5 = 8.077747211

Simplifying
s + 5.5 = 8.077747211

Reorder the terms:
5.5 + s = 8.077747211

Solving
5.5 + s = 8.077747211

Solving for variable 's'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + s = 8.077747211 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + s = 8.077747211 + -5.5
s = 8.077747211 + -5.5

Combine like terms: 8.077747211 + -5.5 = 2.577747211
s = 2.577747211

Simplifying
s = 2.577747211


Subproblem 2
s + 5.5 = -8.077747211

Simplifying
s + 5.5 = -8.077747211

Reorder the terms:
5.5 + s = -8.077747211

Solving
5.5 + s = -8.077747211

Solving for variable 's'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + s = -8.077747211 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + s = -8.077747211 + -5.5
s = -8.077747211 + -5.5

Combine like terms: -8.077747211 + -5.5 = -13.577747211
s = -13.577747211

Simplifying
s = -13.577747211


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {2.577747211, -13.577747211}

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