v^2+16v-31=0

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Solution for v^2+16v-31=0 equation: 


Simplifying
v2 + 16v + -31 = 0

Reorder the terms:
-31 + 16v + v2 = 0

Solving
-31 + 16v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 16v + 31 + v2 = 0 + 31

Reorder the terms:
-31 + 31 + 16v + v2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 16v + v2 = 0 + 31
16v + v2 = 0 + 31

Combine like terms: 0 + 31 = 31
16v + v2 = 31

The v term is 16v.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16v + 64 + v2 = 31 + 64

Reorder the terms:
64 + 16v + v2 = 31 + 64

Combine like terms: 31 + 64 = 95
64 + 16v + v2 = 95

Factor a perfect square on the left side:
(v + 8)(v + 8) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(v + 8) equal to 9.746794345 and -9.746794345.


Subproblem 1
v + 8 = 9.746794345

Simplifying
v + 8 = 9.746794345

Reorder the terms:
8 + v = 9.746794345

Solving
8 + v = 9.746794345

Solving for variable 'v'.

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

Add '-8' to each side of the equation.
8 + -8 + v = 9.746794345 + -8

Combine like terms: 8 + -8 = 0
0 + v = 9.746794345 + -8
v = 9.746794345 + -8

Combine like terms: 9.746794345 + -8 = 1.746794345
v = 1.746794345

Simplifying
v = 1.746794345


Subproblem 2
v + 8 = -9.746794345

Simplifying
v + 8 = -9.746794345

Reorder the terms:
8 + v = -9.746794345

Solving
8 + v = -9.746794345

Solving for variable 'v'.

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

Add '-8' to each side of the equation.
8 + -8 + v = -9.746794345 + -8

Combine like terms: 8 + -8 = 0
0 + v = -9.746794345 + -8
v = -9.746794345 + -8

Combine like terms: -9.746794345 + -8 = -17.746794345
v = -17.746794345

Simplifying
v = -17.746794345


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.746794345, -17.746794345}

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