2v^2-9v-14=(v-4)

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Solution for 2v^2-9v-14=(v-4) equation: 


Simplifying
2v2 + -9v + -14 = (v + -4)

Reorder the terms:
-14 + -9v + 2v2 = (v + -4)

Reorder the terms:
-14 + -9v + 2v2 = (-4 + v)

Remove parenthesis around (-4 + v)
-14 + -9v + 2v2 = -4 + v

Solving
-14 + -9v + 2v2 = -4 + v

Solving for variable 'v'.

Reorder the terms:
-14 + 4 + -9v + -1v + 2v2 = -4 + v + 4 + -1v

Combine like terms: -14 + 4 = -10
-10 + -9v + -1v + 2v2 = -4 + v + 4 + -1v

Combine like terms: -9v + -1v = -10v
-10 + -10v + 2v2 = -4 + v + 4 + -1v

Reorder the terms:
-10 + -10v + 2v2 = -4 + 4 + v + -1v

Combine like terms: -4 + 4 = 0
-10 + -10v + 2v2 = 0 + v + -1v
-10 + -10v + 2v2 = v + -1v

Combine like terms: v + -1v = 0
-10 + -10v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -5v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -5v + v2)' equal to zero and attempt to solve:

Simplifying
-5 + -5v + v2 = 0

Solving
-5 + -5v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -5v + 5 + v2 = 0 + 5

Reorder the terms:
-5 + 5 + -5v + v2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -5v + v2 = 0 + 5
-5v + v2 = 0 + 5

Combine like terms: 0 + 5 = 5
-5v + v2 = 5

The v term is -5v.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5v + 6.25 + v2 = 5 + 6.25

Reorder the terms:
6.25 + -5v + v2 = 5 + 6.25

Combine like terms: 5 + 6.25 = 11.25
6.25 + -5v + v2 = 11.25

Factor a perfect square on the left side:
(v + -2.5)(v + -2.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(v + -2.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
v + -2.5 = 3.354101966

Simplifying
v + -2.5 = 3.354101966

Reorder the terms:
-2.5 + v = 3.354101966

Solving
-2.5 + v = 3.354101966

Solving for variable 'v'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + v = 3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + v = 3.354101966 + 2.5
v = 3.354101966 + 2.5

Combine like terms: 3.354101966 + 2.5 = 5.854101966
v = 5.854101966

Simplifying
v = 5.854101966


Subproblem 2
v + -2.5 = -3.354101966

Simplifying
v + -2.5 = -3.354101966

Reorder the terms:
-2.5 + v = -3.354101966

Solving
-2.5 + v = -3.354101966

Solving for variable 'v'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + v = -3.354101966 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + v = -3.354101966 + 2.5
v = -3.354101966 + 2.5

Combine like terms: -3.354101966 + 2.5 = -0.854101966
v = -0.854101966

Simplifying
v = -0.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {5.854101966, -0.854101966}
Solution
v = {5.854101966, -0.854101966}

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