(v+9)(v+9)-44=0

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Solution for (v+9)(v+9)-44=0 equation: 


Simplifying
(v + 9)(v + 9) + -44 = 0

Reorder the terms:
(9 + v)(v + 9) + -44 = 0

Reorder the terms:
(9 + v)(9 + v) + -44 = 0

Multiply (9 + v) * (9 + v)
(9(9 + v) + v(9 + v)) + -44 = 0
((9 * 9 + v * 9) + v(9 + v)) + -44 = 0
((81 + 9v) + v(9 + v)) + -44 = 0
(81 + 9v + (9 * v + v * v)) + -44 = 0
(81 + 9v + (9v + v2)) + -44 = 0

Combine like terms: 9v + 9v = 18v
(81 + 18v + v2) + -44 = 0

Reorder the terms:
81 + -44 + 18v + v2 = 0

Combine like terms: 81 + -44 = 37
37 + 18v + v2 = 0

Solving
37 + 18v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 18v + -37 + v2 = 0 + -37

Reorder the terms:
37 + -37 + 18v + v2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 18v + v2 = 0 + -37
18v + v2 = 0 + -37

Combine like terms: 0 + -37 = -37
18v + v2 = -37

The v term is 18v.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18v + 81 + v2 = -37 + 81

Reorder the terms:
81 + 18v + v2 = -37 + 81

Combine like terms: -37 + 81 = 44
81 + 18v + v2 = 44

Factor a perfect square on the left side:
(v + 9)(v + 9) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(v + 9) equal to 6.633249581 and -6.633249581.


Subproblem 1
v + 9 = 6.633249581

Simplifying
v + 9 = 6.633249581

Reorder the terms:
9 + v = 6.633249581

Solving
9 + v = 6.633249581

Solving for variable 'v'.

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

Add '-9' to each side of the equation.
9 + -9 + v = 6.633249581 + -9

Combine like terms: 9 + -9 = 0
0 + v = 6.633249581 + -9
v = 6.633249581 + -9

Combine like terms: 6.633249581 + -9 = -2.366750419
v = -2.366750419

Simplifying
v = -2.366750419


Subproblem 2
v + 9 = -6.633249581

Simplifying
v + 9 = -6.633249581

Reorder the terms:
9 + v = -6.633249581

Solving
9 + v = -6.633249581

Solving for variable 'v'.

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

Add '-9' to each side of the equation.
9 + -9 + v = -6.633249581 + -9

Combine like terms: 9 + -9 = 0
0 + v = -6.633249581 + -9
v = -6.633249581 + -9

Combine like terms: -6.633249581 + -9 = -15.633249581
v = -15.633249581

Simplifying
v = -15.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-2.366750419, -15.633249581}

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