v^2-8v-12=0

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Solution for v^2-8v-12=0 equation: 


Simplifying
v2 + -8v + -12 = 0

Reorder the terms:
-12 + -8v + v2 = 0

Solving
-12 + -8v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8v + 12 + v2 = 0 + 12

Reorder the terms:
-12 + 12 + -8v + v2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8v + v2 = 0 + 12
-8v + v2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8v + v2 = 12

The v term is -8v.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8v + 16 + v2 = 12 + 16

Reorder the terms:
16 + -8v + v2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + -8v + v2 = 28

Factor a perfect square on the left side:
(v + -4)(v + -4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(v + -4) equal to 5.291502622 and -5.291502622.


Subproblem 1
v + -4 = 5.291502622

Simplifying
v + -4 = 5.291502622

Reorder the terms:
-4 + v = 5.291502622

Solving
-4 + v = 5.291502622

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = 5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + v = 5.291502622 + 4
v = 5.291502622 + 4

Combine like terms: 5.291502622 + 4 = 9.291502622
v = 9.291502622

Simplifying
v = 9.291502622


Subproblem 2
v + -4 = -5.291502622

Simplifying
v + -4 = -5.291502622

Reorder the terms:
-4 + v = -5.291502622

Solving
-4 + v = -5.291502622

Solving for variable 'v'.

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

Add '4' to each side of the equation.
-4 + 4 + v = -5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + v = -5.291502622 + 4
v = -5.291502622 + 4

Combine like terms: -5.291502622 + 4 = -1.291502622
v = -1.291502622

Simplifying
v = -1.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {9.291502622, -1.291502622}

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