3v^2+44v+49=0

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Solution for 3v^2+44v+49=0 equation: 


Simplifying
3v2 + 44v + 49 = 0

Reorder the terms:
49 + 44v + 3v2 = 0

Solving
49 + 44v + 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 + 14.66666667v + v2 = 0

Move the constant term to the right:

Add '-16.33333333' to each side of the equation.
16.33333333 + 14.66666667v + -16.33333333 + v2 = 0 + -16.33333333

Reorder the terms:
16.33333333 + -16.33333333 + 14.66666667v + v2 = 0 + -16.33333333

Combine like terms: 16.33333333 + -16.33333333 = 0.00000000
0.00000000 + 14.66666667v + v2 = 0 + -16.33333333
14.66666667v + v2 = 0 + -16.33333333

Combine like terms: 0 + -16.33333333 = -16.33333333
14.66666667v + v2 = -16.33333333

The v term is 14.66666667v.  Take half its coefficient (7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
14.66666667v + 53.77777780 + v2 = -16.33333333 + 53.77777780

Reorder the terms:
53.77777780 + 14.66666667v + v2 = -16.33333333 + 53.77777780

Combine like terms: -16.33333333 + 53.77777780 = 37.44444447
53.77777780 + 14.66666667v + v2 = 37.44444447

Factor a perfect square on the left side:
(v + 7.333333335)(v + 7.333333335) = 37.44444447

Calculate the square root of the right side: 6.119186586

Break this problem into two subproblems by setting 
(v + 7.333333335) equal to 6.119186586 and -6.119186586.


Subproblem 1
v + 7.333333335 = 6.119186586

Simplifying
v + 7.333333335 = 6.119186586

Reorder the terms:
7.333333335 + v = 6.119186586

Solving
7.333333335 + v = 6.119186586

Solving for variable 'v'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + v = 6.119186586 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + v = 6.119186586 + -7.333333335
v = 6.119186586 + -7.333333335

Combine like terms: 6.119186586 + -7.333333335 = -1.214146749
v = -1.214146749

Simplifying
v = -1.214146749


Subproblem 2
v + 7.333333335 = -6.119186586

Simplifying
v + 7.333333335 = -6.119186586

Reorder the terms:
7.333333335 + v = -6.119186586

Solving
7.333333335 + v = -6.119186586

Solving for variable 'v'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + v = -6.119186586 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + v = -6.119186586 + -7.333333335
v = -6.119186586 + -7.333333335

Combine like terms: -6.119186586 + -7.333333335 = -13.452519921
v = -13.452519921

Simplifying
v = -13.452519921


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-1.214146749, -13.452519921}

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