4v^2-4v-96=0

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Solution for 4v^2-4v-96=0 equation: 


Simplifying
4v2 + -4v + -96 = 0

Reorder the terms:
-96 + -4v + 4v2 = 0

Solving
-96 + -4v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -1v + v2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-24 + -1v + v2)' equal to zero and attempt to solve:

Simplifying
-24 + -1v + v2 = 0

Solving
-24 + -1v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -1v + 24 + v2 = 0 + 24

Reorder the terms:
-24 + 24 + -1v + v2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1v + v2 = 0 + 24
-1v + v2 = 0 + 24

Combine like terms: 0 + 24 = 24
-1v + v2 = 24

The v term is -1v.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1v + 0.25 + v2 = 24 + 0.25

Reorder the terms:
0.25 + -1v + v2 = 24 + 0.25

Combine like terms: 24 + 0.25 = 24.25
0.25 + -1v + v2 = 24.25

Factor a perfect square on the left side:
(v + -0.5)(v + -0.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(v + -0.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
v + -0.5 = 4.924428901

Simplifying
v + -0.5 = 4.924428901

Reorder the terms:
-0.5 + v = 4.924428901

Solving
-0.5 + v = 4.924428901

Solving for variable 'v'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + v = 4.924428901 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + v = 4.924428901 + 0.5
v = 4.924428901 + 0.5

Combine like terms: 4.924428901 + 0.5 = 5.424428901
v = 5.424428901

Simplifying
v = 5.424428901


Subproblem 2
v + -0.5 = -4.924428901

Simplifying
v + -0.5 = -4.924428901

Reorder the terms:
-0.5 + v = -4.924428901

Solving
-0.5 + v = -4.924428901

Solving for variable 'v'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + v = -4.924428901 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + v = -4.924428901 + 0.5
v = -4.924428901 + 0.5

Combine like terms: -4.924428901 + 0.5 = -4.424428901
v = -4.424428901

Simplifying
v = -4.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {5.424428901, -4.424428901}
Solution
v = {5.424428901, -4.424428901}

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