v^2-14v-44=0

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Solution for v^2-14v-44=0 equation: 


Simplifying
v2 + -14v + -44 = 0

Reorder the terms:
-44 + -14v + v2 = 0

Solving
-44 + -14v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -14v + 44 + v2 = 0 + 44

Reorder the terms:
-44 + 44 + -14v + v2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -14v + v2 = 0 + 44
-14v + v2 = 0 + 44

Combine like terms: 0 + 44 = 44
-14v + v2 = 44

The v term is -14v.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14v + 49 + v2 = 44 + 49

Reorder the terms:
49 + -14v + v2 = 44 + 49

Combine like terms: 44 + 49 = 93
49 + -14v + v2 = 93

Factor a perfect square on the left side:
(v + -7)(v + -7) = 93

Calculate the square root of the right side: 9.643650761

Break this problem into two subproblems by setting 
(v + -7) equal to 9.643650761 and -9.643650761.


Subproblem 1
v + -7 = 9.643650761

Simplifying
v + -7 = 9.643650761

Reorder the terms:
-7 + v = 9.643650761

Solving
-7 + v = 9.643650761

Solving for variable 'v'.

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

Add '7' to each side of the equation.
-7 + 7 + v = 9.643650761 + 7

Combine like terms: -7 + 7 = 0
0 + v = 9.643650761 + 7
v = 9.643650761 + 7

Combine like terms: 9.643650761 + 7 = 16.643650761
v = 16.643650761

Simplifying
v = 16.643650761


Subproblem 2
v + -7 = -9.643650761

Simplifying
v + -7 = -9.643650761

Reorder the terms:
-7 + v = -9.643650761

Solving
-7 + v = -9.643650761

Solving for variable 'v'.

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

Add '7' to each side of the equation.
-7 + 7 + v = -9.643650761 + 7

Combine like terms: -7 + 7 = 0
0 + v = -9.643650761 + 7
v = -9.643650761 + 7

Combine like terms: -9.643650761 + 7 = -2.643650761
v = -2.643650761

Simplifying
v = -2.643650761


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {16.643650761, -2.643650761}

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