3v^2+29v+58=0

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Solution for 3v^2+29v+58=0 equation: 


Simplifying
3v2 + 29v + 58 = 0

Reorder the terms:
58 + 29v + 3v2 = 0

Solving
58 + 29v + 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'.
19.33333333 + 9.666666667v + v2 = 0

Move the constant term to the right:

Add '-19.33333333' to each side of the equation.
19.33333333 + 9.666666667v + -19.33333333 + v2 = 0 + -19.33333333

Reorder the terms:
19.33333333 + -19.33333333 + 9.666666667v + v2 = 0 + -19.33333333

Combine like terms: 19.33333333 + -19.33333333 = 0.00000000
0.00000000 + 9.666666667v + v2 = 0 + -19.33333333
9.666666667v + v2 = 0 + -19.33333333

Combine like terms: 0 + -19.33333333 = -19.33333333
9.666666667v + v2 = -19.33333333

The v term is 9.666666667v.  Take half its coefficient (4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
9.666666667v + 23.36111112 + v2 = -19.33333333 + 23.36111112

Reorder the terms:
23.36111112 + 9.666666667v + v2 = -19.33333333 + 23.36111112

Combine like terms: -19.33333333 + 23.36111112 = 4.02777779
23.36111112 + 9.666666667v + v2 = 4.02777779

Factor a perfect square on the left side:
(v + 4.833333334)(v + 4.833333334) = 4.02777779

Calculate the square root of the right side: 2.006932433

Break this problem into two subproblems by setting 
(v + 4.833333334) equal to 2.006932433 and -2.006932433.


Subproblem 1
v + 4.833333334 = 2.006932433

Simplifying
v + 4.833333334 = 2.006932433

Reorder the terms:
4.833333334 + v = 2.006932433

Solving
4.833333334 + v = 2.006932433

Solving for variable 'v'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + v = 2.006932433 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + v = 2.006932433 + -4.833333334
v = 2.006932433 + -4.833333334

Combine like terms: 2.006932433 + -4.833333334 = -2.826400901
v = -2.826400901

Simplifying
v = -2.826400901


Subproblem 2
v + 4.833333334 = -2.006932433

Simplifying
v + 4.833333334 = -2.006932433

Reorder the terms:
4.833333334 + v = -2.006932433

Solving
4.833333334 + v = -2.006932433

Solving for variable 'v'.

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

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + v = -2.006932433 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + v = -2.006932433 + -4.833333334
v = -2.006932433 + -4.833333334

Combine like terms: -2.006932433 + -4.833333334 = -6.840265767
v = -6.840265767

Simplifying
v = -6.840265767


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-2.826400901, -6.840265767}

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