v^2+20v+46=0

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Solution for v^2+20v+46=0 equation: 


Simplifying
v2 + 20v + 46 = 0

Reorder the terms:
46 + 20v + v2 = 0

Solving
46 + 20v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + 20v + -46 + v2 = 0 + -46

Reorder the terms:
46 + -46 + 20v + v2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 20v + v2 = 0 + -46
20v + v2 = 0 + -46

Combine like terms: 0 + -46 = -46
20v + v2 = -46

The v term is 20v.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20v + 100 + v2 = -46 + 100

Reorder the terms:
100 + 20v + v2 = -46 + 100

Combine like terms: -46 + 100 = 54
100 + 20v + v2 = 54

Factor a perfect square on the left side:
(v + 10)(v + 10) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(v + 10) equal to 7.348469228 and -7.348469228.


Subproblem 1
v + 10 = 7.348469228

Simplifying
v + 10 = 7.348469228

Reorder the terms:
10 + v = 7.348469228

Solving
10 + v = 7.348469228

Solving for variable 'v'.

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

Add '-10' to each side of the equation.
10 + -10 + v = 7.348469228 + -10

Combine like terms: 10 + -10 = 0
0 + v = 7.348469228 + -10
v = 7.348469228 + -10

Combine like terms: 7.348469228 + -10 = -2.651530772
v = -2.651530772

Simplifying
v = -2.651530772


Subproblem 2
v + 10 = -7.348469228

Simplifying
v + 10 = -7.348469228

Reorder the terms:
10 + v = -7.348469228

Solving
10 + v = -7.348469228

Solving for variable 'v'.

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

Add '-10' to each side of the equation.
10 + -10 + v = -7.348469228 + -10

Combine like terms: 10 + -10 = 0
0 + v = -7.348469228 + -10
v = -7.348469228 + -10

Combine like terms: -7.348469228 + -10 = -17.348469228
v = -17.348469228

Simplifying
v = -17.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-2.651530772, -17.348469228}

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