v^2+11v+11=0

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Solution for v^2+11v+11=0 equation: 


Simplifying
v2 + 11v + 11 = 0

Reorder the terms:
11 + 11v + v2 = 0

Solving
11 + 11v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 11v + -11 + v2 = 0 + -11

Reorder the terms:
11 + -11 + 11v + v2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 11v + v2 = 0 + -11
11v + v2 = 0 + -11

Combine like terms: 0 + -11 = -11
11v + v2 = -11

The v term is 11v.  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.
11v + 30.25 + v2 = -11 + 30.25

Reorder the terms:
30.25 + 11v + v2 = -11 + 30.25

Combine like terms: -11 + 30.25 = 19.25
30.25 + 11v + v2 = 19.25

Factor a perfect square on the left side:
(v + 5.5)(v + 5.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(v + 5.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
v + 5.5 = 4.387482194

Simplifying
v + 5.5 = 4.387482194

Reorder the terms:
5.5 + v = 4.387482194

Solving
5.5 + v = 4.387482194

Solving for variable 'v'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + v = 4.387482194 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + v = 4.387482194 + -5.5
v = 4.387482194 + -5.5

Combine like terms: 4.387482194 + -5.5 = -1.112517806
v = -1.112517806

Simplifying
v = -1.112517806


Subproblem 2
v + 5.5 = -4.387482194

Simplifying
v + 5.5 = -4.387482194

Reorder the terms:
5.5 + v = -4.387482194

Solving
5.5 + v = -4.387482194

Solving for variable 'v'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + v = -4.387482194 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + v = -4.387482194 + -5.5
v = -4.387482194 + -5.5

Combine like terms: -4.387482194 + -5.5 = -9.887482194
v = -9.887482194

Simplifying
v = -9.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-1.112517806, -9.887482194}

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