v^2+12v-54=5

Solution for v^2+12v-54=5 equation:

Simplifying
v2 + 12v + -54 = 5

Reorder the terms:
-54 + 12v + v2 = 5

Solving
-54 + 12v + v2 = 5

Solving for variable 'v'.

Reorder the terms:
-54 + -5 + 12v + v2 = 5 + -5

Combine like terms: -54 + -5 = -59
-59 + 12v + v2 = 5 + -5

Combine like terms: 5 + -5 = 0
-59 + 12v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 12v + 59 + v2 = 0 + 59

Reorder the terms:
-59 + 59 + 12v + v2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 12v + v2 = 0 + 59
12v + v2 = 0 + 59

Combine like terms: 0 + 59 = 59
12v + v2 = 59

The v term is 12v.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12v + 36 + v2 = 59 + 36

Reorder the terms:
36 + 12v + v2 = 59 + 36

Combine like terms: 59 + 36 = 95
36 + 12v + v2 = 95

Factor a perfect square on the left side:
(v + 6)(v + 6) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(v + 6) equal to 9.746794345 and -9.746794345.

Subproblem 1
v + 6 = 9.746794345

Simplifying
v + 6 = 9.746794345

Reorder the terms:
6 + v = 9.746794345

Solving
6 + v = 9.746794345

Solving for variable 'v'.

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

Add '-6' to each side of the equation.
6 + -6 + v = 9.746794345 + -6

Combine like terms: 6 + -6 = 0
0 + v = 9.746794345 + -6
v = 9.746794345 + -6

Combine like terms: 9.746794345 + -6 = 3.746794345
v = 3.746794345

Simplifying
v = 3.746794345

Subproblem 2
v + 6 = -9.746794345

Simplifying
v + 6 = -9.746794345

Reorder the terms:
6 + v = -9.746794345

Solving
6 + v = -9.746794345

Solving for variable 'v'.

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

Add '-6' to each side of the equation.
6 + -6 + v = -9.746794345 + -6

Combine like terms: 6 + -6 = 0
0 + v = -9.746794345 + -6
v = -9.746794345 + -6

Combine like terms: -9.746794345 + -6 = -15.746794345
v = -15.746794345

Simplifying
v = -15.746794345

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.746794345, -15.746794345}