v^2-6v-3=0

Solution for v^2-6v-3=0 equation:

Simplifying
v2 + -6v + -3 = 0

Reorder the terms:
-3 + -6v + v2 = 0

Solving
-3 + -6v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6v + 3 + v2 = 0 + 3

Reorder the terms:
-3 + 3 + -6v + v2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6v + v2 = 0 + 3
-6v + v2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6v + v2 = 3

The v term is -6v.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6v + 9 + v2 = 3 + 9

Reorder the terms:
9 + -6v + v2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + -6v + v2 = 12

Factor a perfect square on the left side:
(v + -3)(v + -3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(v + -3) equal to 3.464101615 and -3.464101615.

Subproblem 1
v + -3 = 3.464101615

Simplifying
v + -3 = 3.464101615

Reorder the terms:
-3 + v = 3.464101615

Solving
-3 + v = 3.464101615

Solving for variable 'v'.

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

Add '3' to each side of the equation.
-3 + 3 + v = 3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + v = 3.464101615 + 3
v = 3.464101615 + 3

Combine like terms: 3.464101615 + 3 = 6.464101615
v = 6.464101615

Simplifying
v = 6.464101615

Subproblem 2
v + -3 = -3.464101615

Simplifying
v + -3 = -3.464101615

Reorder the terms:
-3 + v = -3.464101615

Solving
-3 + v = -3.464101615

Solving for variable 'v'.

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

Add '3' to each side of the equation.
-3 + 3 + v = -3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + v = -3.464101615 + 3
v = -3.464101615 + 3

Combine like terms: -3.464101615 + 3 = -0.464101615
v = -0.464101615

Simplifying
v = -0.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.464101615, -0.464101615}