4v^2-64v+28=0

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Solution for 4v^2-64v+28=0 equation: 


Simplifying
4v2 + -64v + 28 = 0

Reorder the terms:
28 + -64v + 4v2 = 0

Solving
28 + -64v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -16v + v2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + -16v + v2)' equal to zero and attempt to solve:

Simplifying
7 + -16v + v2 = 0

Solving
7 + -16v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -16v + -7 + v2 = 0 + -7

Reorder the terms:
7 + -7 + -16v + v2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -16v + v2 = 0 + -7
-16v + v2 = 0 + -7

Combine like terms: 0 + -7 = -7
-16v + v2 = -7

The v term is -16v.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16v + 64 + v2 = -7 + 64

Reorder the terms:
64 + -16v + v2 = -7 + 64

Combine like terms: -7 + 64 = 57
64 + -16v + v2 = 57

Factor a perfect square on the left side:
(v + -8)(v + -8) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(v + -8) equal to 7.549834435 and -7.549834435.


Subproblem 1
v + -8 = 7.549834435

Simplifying
v + -8 = 7.549834435

Reorder the terms:
-8 + v = 7.549834435

Solving
-8 + v = 7.549834435

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + v = 7.549834435 + 8

Combine like terms: -8 + 8 = 0
0 + v = 7.549834435 + 8
v = 7.549834435 + 8

Combine like terms: 7.549834435 + 8 = 15.549834435
v = 15.549834435

Simplifying
v = 15.549834435


Subproblem 2
v + -8 = -7.549834435

Simplifying
v + -8 = -7.549834435

Reorder the terms:
-8 + v = -7.549834435

Solving
-8 + v = -7.549834435

Solving for variable 'v'.

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

Add '8' to each side of the equation.
-8 + 8 + v = -7.549834435 + 8

Combine like terms: -8 + 8 = 0
0 + v = -7.549834435 + 8
v = -7.549834435 + 8

Combine like terms: -7.549834435 + 8 = 0.450165565
v = 0.450165565

Simplifying
v = 0.450165565


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {15.549834435, 0.450165565}
Solution
v = {15.549834435, 0.450165565}

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