4v^2-32v-44=0

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Solution for 4v^2-32v-44=0 equation: 


Simplifying
4v2 + -32v + -44 = 0

Reorder the terms:
-44 + -32v + 4v2 = 0

Solving
-44 + -32v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + -8v + v2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + -8v + v2)' equal to zero and attempt to solve:

Simplifying
-11 + -8v + v2 = 0

Solving
-11 + -8v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -8v + 11 + v2 = 0 + 11

Reorder the terms:
-11 + 11 + -8v + v2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -8v + v2 = 0 + 11
-8v + v2 = 0 + 11

Combine like terms: 0 + 11 = 11
-8v + v2 = 11

The v term is -8v.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8v + 16 + v2 = 11 + 16

Reorder the terms:
16 + -8v + v2 = 11 + 16

Combine like terms: 11 + 16 = 27
16 + -8v + v2 = 27

Factor a perfect square on the left side:
(v + -4)(v + -4) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(v + -4) equal to 5.196152423 and -5.196152423.


Subproblem 1
v + -4 = 5.196152423

Simplifying
v + -4 = 5.196152423

Reorder the terms:
-4 + v = 5.196152423

Solving
-4 + v = 5.196152423

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = 5.196152423 + 4

Combine like terms: -4 + 4 = 0
0 + v = 5.196152423 + 4
v = 5.196152423 + 4

Combine like terms: 5.196152423 + 4 = 9.196152423
v = 9.196152423

Simplifying
v = 9.196152423


Subproblem 2
v + -4 = -5.196152423

Simplifying
v + -4 = -5.196152423

Reorder the terms:
-4 + v = -5.196152423

Solving
-4 + v = -5.196152423

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = -5.196152423 + 4

Combine like terms: -4 + 4 = 0
0 + v = -5.196152423 + 4
v = -5.196152423 + 4

Combine like terms: -5.196152423 + 4 = -1.196152423
v = -1.196152423

Simplifying
v = -1.196152423


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {9.196152423, -1.196152423}
Solution
v = {9.196152423, -1.196152423}

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