2(v-7)4v=-22

Solution for 2(v-7)4v=-22 equation:

Simplifying
2(v + -7) * 4v = -22

Reorder the terms:
2(-7 + v) * 4v = -22

Reorder the terms for easier multiplication:
2 * 4v(-7 + v) = -22

Multiply 2 * 4
8v(-7 + v) = -22
(-7 * 8v + v * 8v) = -22
(-56v + 8v2) = -22

Solving
-56v + 8v2 = -22

Solving for variable 'v'.

Reorder the terms:
22 + -56v + 8v2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + -56v + 8v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -28v + 4v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + -28v + 4v2)' equal to zero and attempt to solve:

Simplifying
11 + -28v + 4v2 = 0

Solving
11 + -28v + 4v2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
2.75 + -7v + v2 = 0

Move the constant term to the right:

Add '-2.75' to each side of the equation.
2.75 + -7v + -2.75 + v2 = 0 + -2.75

Reorder the terms:
2.75 + -2.75 + -7v + v2 = 0 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + -7v + v2 = 0 + -2.75
-7v + v2 = 0 + -2.75

Combine like terms: 0 + -2.75 = -2.75
-7v + v2 = -2.75

The v term is -7v.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7v + 12.25 + v2 = -2.75 + 12.25

Reorder the terms:
12.25 + -7v + v2 = -2.75 + 12.25

Combine like terms: -2.75 + 12.25 = 9.5
12.25 + -7v + v2 = 9.5

Factor a perfect square on the left side:
(v + -3.5)(v + -3.5) = 9.5

Calculate the square root of the right side: 3.082207001

Break this problem into two subproblems by setting 
(v + -3.5) equal to 3.082207001 and -3.082207001.

Subproblem 1
v + -3.5 = 3.082207001

Simplifying
v + -3.5 = 3.082207001

Reorder the terms:
-3.5 + v = 3.082207001

Solving
-3.5 + v = 3.082207001

Solving for variable 'v'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + v = 3.082207001 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + v = 3.082207001 + 3.5
v = 3.082207001 + 3.5

Combine like terms: 3.082207001 + 3.5 = 6.582207001
v = 6.582207001

Simplifying
v = 6.582207001

Subproblem 2
v + -3.5 = -3.082207001

Simplifying
v + -3.5 = -3.082207001

Reorder the terms:
-3.5 + v = -3.082207001

Solving
-3.5 + v = -3.082207001

Solving for variable 'v'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + v = -3.082207001 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + v = -3.082207001 + 3.5
v = -3.082207001 + 3.5

Combine like terms: -3.082207001 + 3.5 = 0.417792999
v = 0.417792999

Simplifying
v = 0.417792999

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.582207001, 0.417792999}
Solution
v = {6.582207001, 0.417792999}