3v^2+26v-45=0

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Solution for 3v^2+26v-45=0 equation: 


Simplifying
3v2 + 26v + -45 = 0

Reorder the terms:
-45 + 26v + 3v2 = 0

Solving
-45 + 26v + 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'.
-15 + 8.666666667v + v2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8.666666667v + 15 + v2 = 0 + 15

Reorder the terms:
-15 + 15 + 8.666666667v + v2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8.666666667v + v2 = 0 + 15
8.666666667v + v2 = 0 + 15

Combine like terms: 0 + 15 = 15
8.666666667v + v2 = 15

The v term is 8.666666667v.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667v + 18.77777778 + v2 = 15 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667v + v2 = 15 + 18.77777778

Combine like terms: 15 + 18.77777778 = 33.77777778
18.77777778 + 8.666666667v + v2 = 33.77777778

Factor a perfect square on the left side:
(v + 4.333333334)(v + 4.333333334) = 33.77777778

Calculate the square root of the right side: 5.811865258

Break this problem into two subproblems by setting 
(v + 4.333333334) equal to 5.811865258 and -5.811865258.


Subproblem 1
v + 4.333333334 = 5.811865258

Simplifying
v + 4.333333334 = 5.811865258

Reorder the terms:
4.333333334 + v = 5.811865258

Solving
4.333333334 + v = 5.811865258

Solving for variable 'v'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + v = 5.811865258 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + v = 5.811865258 + -4.333333334
v = 5.811865258 + -4.333333334

Combine like terms: 5.811865258 + -4.333333334 = 1.478531924
v = 1.478531924

Simplifying
v = 1.478531924


Subproblem 2
v + 4.333333334 = -5.811865258

Simplifying
v + 4.333333334 = -5.811865258

Reorder the terms:
4.333333334 + v = -5.811865258

Solving
4.333333334 + v = -5.811865258

Solving for variable 'v'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + v = -5.811865258 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + v = -5.811865258 + -4.333333334
v = -5.811865258 + -4.333333334

Combine like terms: -5.811865258 + -4.333333334 = -10.145198592
v = -10.145198592

Simplifying
v = -10.145198592


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.478531924, -10.145198592}

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