v^2+22v-2672=0

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Solution for v^2+22v-2672=0 equation: 


Simplifying
v2 + 22v + -2672 = 0

Reorder the terms:
-2672 + 22v + v2 = 0

Solving
-2672 + 22v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '2672' to each side of the equation.
-2672 + 22v + 2672 + v2 = 0 + 2672

Reorder the terms:
-2672 + 2672 + 22v + v2 = 0 + 2672

Combine like terms: -2672 + 2672 = 0
0 + 22v + v2 = 0 + 2672
22v + v2 = 0 + 2672

Combine like terms: 0 + 2672 = 2672
22v + v2 = 2672

The v term is 22v.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22v + 121 + v2 = 2672 + 121

Reorder the terms:
121 + 22v + v2 = 2672 + 121

Combine like terms: 2672 + 121 = 2793
121 + 22v + v2 = 2793

Factor a perfect square on the left side:
(v + 11)(v + 11) = 2793

Calculate the square root of the right side: 52.848841047

Break this problem into two subproblems by setting 
(v + 11) equal to 52.848841047 and -52.848841047.


Subproblem 1
v + 11 = 52.848841047

Simplifying
v + 11 = 52.848841047

Reorder the terms:
11 + v = 52.848841047

Solving
11 + v = 52.848841047

Solving for variable 'v'.

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

Add '-11' to each side of the equation.
11 + -11 + v = 52.848841047 + -11

Combine like terms: 11 + -11 = 0
0 + v = 52.848841047 + -11
v = 52.848841047 + -11

Combine like terms: 52.848841047 + -11 = 41.848841047
v = 41.848841047

Simplifying
v = 41.848841047


Subproblem 2
v + 11 = -52.848841047

Simplifying
v + 11 = -52.848841047

Reorder the terms:
11 + v = -52.848841047

Solving
11 + v = -52.848841047

Solving for variable 'v'.

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

Add '-11' to each side of the equation.
11 + -11 + v = -52.848841047 + -11

Combine like terms: 11 + -11 = 0
0 + v = -52.848841047 + -11
v = -52.848841047 + -11

Combine like terms: -52.848841047 + -11 = -63.848841047
v = -63.848841047

Simplifying
v = -63.848841047


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {41.848841047, -63.848841047}

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