v^2-2v-13=0

Solution for v^2-2v-13=0 equation:

Simplifying
v2 + -2v + -13 = 0

Reorder the terms:
-13 + -2v + v2 = 0

Solving
-13 + -2v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -2v + 13 + v2 = 0 + 13

Reorder the terms:
-13 + 13 + -2v + v2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2v + v2 = 0 + 13
-2v + v2 = 0 + 13

Combine like terms: 0 + 13 = 13
-2v + v2 = 13

The v term is -2v.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2v + 1 + v2 = 13 + 1

Reorder the terms:
1 + -2v + v2 = 13 + 1

Combine like terms: 13 + 1 = 14
1 + -2v + v2 = 14

Factor a perfect square on the left side:
(v + -1)(v + -1) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(v + -1) equal to 3.741657387 and -3.741657387.

Subproblem 1
v + -1 = 3.741657387

Simplifying
v + -1 = 3.741657387

Reorder the terms:
-1 + v = 3.741657387

Solving
-1 + v = 3.741657387

Solving for variable 'v'.

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

Add '1' to each side of the equation.
-1 + 1 + v = 3.741657387 + 1

Combine like terms: -1 + 1 = 0
0 + v = 3.741657387 + 1
v = 3.741657387 + 1

Combine like terms: 3.741657387 + 1 = 4.741657387
v = 4.741657387

Simplifying
v = 4.741657387

Subproblem 2
v + -1 = -3.741657387

Simplifying
v + -1 = -3.741657387

Reorder the terms:
-1 + v = -3.741657387

Solving
-1 + v = -3.741657387

Solving for variable 'v'.

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

Add '1' to each side of the equation.
-1 + 1 + v = -3.741657387 + 1

Combine like terms: -1 + 1 = 0
0 + v = -3.741657387 + 1
v = -3.741657387 + 1

Combine like terms: -3.741657387 + 1 = -2.741657387
v = -2.741657387

Simplifying
v = -2.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.741657387, -2.741657387}