3v^2+38v+49=0

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Solution for 3v^2+38v+49=0 equation: 


Simplifying
3v2 + 38v + 49 = 0

Reorder the terms:
49 + 38v + 3v2 = 0

Solving
49 + 38v + 3v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
16.33333333 + 12.66666667v + v2 = 0

Move the constant term to the right:

Add '-16.33333333' to each side of the equation.
16.33333333 + 12.66666667v + -16.33333333 + v2 = 0 + -16.33333333

Reorder the terms:
16.33333333 + -16.33333333 + 12.66666667v + v2 = 0 + -16.33333333

Combine like terms: 16.33333333 + -16.33333333 = 0.00000000
0.00000000 + 12.66666667v + v2 = 0 + -16.33333333
12.66666667v + v2 = 0 + -16.33333333

Combine like terms: 0 + -16.33333333 = -16.33333333
12.66666667v + v2 = -16.33333333

The v term is 12.66666667v.  Take half its coefficient (6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
12.66666667v + 40.11111113 + v2 = -16.33333333 + 40.11111113

Reorder the terms:
40.11111113 + 12.66666667v + v2 = -16.33333333 + 40.11111113

Combine like terms: -16.33333333 + 40.11111113 = 23.7777778
40.11111113 + 12.66666667v + v2 = 23.7777778

Factor a perfect square on the left side:
(v + 6.333333335)(v + 6.333333335) = 23.7777778

Calculate the square root of the right side: 4.876246282

Break this problem into two subproblems by setting 
(v + 6.333333335) equal to 4.876246282 and -4.876246282.


Subproblem 1
v + 6.333333335 = 4.876246282

Simplifying
v + 6.333333335 = 4.876246282

Reorder the terms:
6.333333335 + v = 4.876246282

Solving
6.333333335 + v = 4.876246282

Solving for variable 'v'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + v = 4.876246282 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + v = 4.876246282 + -6.333333335
v = 4.876246282 + -6.333333335

Combine like terms: 4.876246282 + -6.333333335 = -1.457087053
v = -1.457087053

Simplifying
v = -1.457087053


Subproblem 2
v + 6.333333335 = -4.876246282

Simplifying
v + 6.333333335 = -4.876246282

Reorder the terms:
6.333333335 + v = -4.876246282

Solving
6.333333335 + v = -4.876246282

Solving for variable 'v'.

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

Add '-6.333333335' to each side of the equation.
6.333333335 + -6.333333335 + v = -4.876246282 + -6.333333335

Combine like terms: 6.333333335 + -6.333333335 = 0.000000000
0.000000000 + v = -4.876246282 + -6.333333335
v = -4.876246282 + -6.333333335

Combine like terms: -4.876246282 + -6.333333335 = -11.209579617
v = -11.209579617

Simplifying
v = -11.209579617


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-1.457087053, -11.209579617}

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