v^2+11v-25=0

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Solution for v^2+11v-25=0 equation: 


Simplifying
v2 + 11v + -25 = 0

Reorder the terms:
-25 + 11v + v2 = 0

Solving
-25 + 11v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 11v + 25 + v2 = 0 + 25

Reorder the terms:
-25 + 25 + 11v + v2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 11v + v2 = 0 + 25
11v + v2 = 0 + 25

Combine like terms: 0 + 25 = 25
11v + v2 = 25

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 = 25 + 30.25

Reorder the terms:
30.25 + 11v + v2 = 25 + 30.25

Combine like terms: 25 + 30.25 = 55.25
30.25 + 11v + v2 = 55.25

Factor a perfect square on the left side:
(v + 5.5)(v + 5.5) = 55.25

Calculate the square root of the right side: 7.433034374

Break this problem into two subproblems by setting 
(v + 5.5) equal to 7.433034374 and -7.433034374.


Subproblem 1
v + 5.5 = 7.433034374

Simplifying
v + 5.5 = 7.433034374

Reorder the terms:
5.5 + v = 7.433034374

Solving
5.5 + v = 7.433034374

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 = 7.433034374 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + v = 7.433034374 + -5.5
v = 7.433034374 + -5.5

Combine like terms: 7.433034374 + -5.5 = 1.933034374
v = 1.933034374

Simplifying
v = 1.933034374


Subproblem 2
v + 5.5 = -7.433034374

Simplifying
v + 5.5 = -7.433034374

Reorder the terms:
5.5 + v = -7.433034374

Solving
5.5 + v = -7.433034374

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 = -7.433034374 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + v = -7.433034374 + -5.5
v = -7.433034374 + -5.5

Combine like terms: -7.433034374 + -5.5 = -12.933034374
v = -12.933034374

Simplifying
v = -12.933034374


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.933034374, -12.933034374}

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