v^2-4v-80=0

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Solution for v^2-4v-80=0 equation: 


Simplifying
v2 + -4v + -80 = 0

Reorder the terms:
-80 + -4v + v2 = 0

Solving
-80 + -4v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -4v + 80 + v2 = 0 + 80

Reorder the terms:
-80 + 80 + -4v + v2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -4v + v2 = 0 + 80
-4v + v2 = 0 + 80

Combine like terms: 0 + 80 = 80
-4v + v2 = 80

The v term is -4v.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4v + 4 + v2 = 80 + 4

Reorder the terms:
4 + -4v + v2 = 80 + 4

Combine like terms: 80 + 4 = 84
4 + -4v + v2 = 84

Factor a perfect square on the left side:
(v + -2)(v + -2) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(v + -2) equal to 9.16515139 and -9.16515139.


Subproblem 1
v + -2 = 9.16515139

Simplifying
v + -2 = 9.16515139

Reorder the terms:
-2 + v = 9.16515139

Solving
-2 + v = 9.16515139

Solving for variable 'v'.

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

Add '2' to each side of the equation.
-2 + 2 + v = 9.16515139 + 2

Combine like terms: -2 + 2 = 0
0 + v = 9.16515139 + 2
v = 9.16515139 + 2

Combine like terms: 9.16515139 + 2 = 11.16515139
v = 11.16515139

Simplifying
v = 11.16515139


Subproblem 2
v + -2 = -9.16515139

Simplifying
v + -2 = -9.16515139

Reorder the terms:
-2 + v = -9.16515139

Solving
-2 + v = -9.16515139

Solving for variable 'v'.

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

Add '2' to each side of the equation.
-2 + 2 + v = -9.16515139 + 2

Combine like terms: -2 + 2 = 0
0 + v = -9.16515139 + 2
v = -9.16515139 + 2

Combine like terms: -9.16515139 + 2 = -7.16515139
v = -7.16515139

Simplifying
v = -7.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {11.16515139, -7.16515139}

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