v(3v-17)=-23

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Solution for v(3v-17)=-23 equation: 


Simplifying
v(3v + -17) = -23

Reorder the terms:
v(-17 + 3v) = -23
(-17 * v + 3v * v) = -23
(-17v + 3v2) = -23

Solving
-17v + 3v2 = -23

Solving for variable 'v'.

Reorder the terms:
23 + -17v + 3v2 = -23 + 23

Combine like terms: -23 + 23 = 0
23 + -17v + 3v2 = 0

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

Divide each side by '3'.
7.666666667 + -5.666666667v + v2 = 0

Move the constant term to the right:

Add '-7.666666667' to each side of the equation.
7.666666667 + -5.666666667v + -7.666666667 + v2 = 0 + -7.666666667

Reorder the terms:
7.666666667 + -7.666666667 + -5.666666667v + v2 = 0 + -7.666666667

Combine like terms: 7.666666667 + -7.666666667 = 0.000000000
0.000000000 + -5.666666667v + v2 = 0 + -7.666666667
-5.666666667v + v2 = 0 + -7.666666667

Combine like terms: 0 + -7.666666667 = -7.666666667
-5.666666667v + v2 = -7.666666667

The v term is -5.666666667v.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667v + 8.027777782 + v2 = -7.666666667 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667v + v2 = -7.666666667 + 8.027777782

Combine like terms: -7.666666667 + 8.027777782 = 0.361111115
8.027777782 + -5.666666667v + v2 = 0.361111115

Factor a perfect square on the left side:
(v + -2.833333334)(v + -2.833333334) = 0.361111115

Calculate the square root of the right side: 0.600925216

Break this problem into two subproblems by setting 
(v + -2.833333334) equal to 0.600925216 and -0.600925216.


Subproblem 1
v + -2.833333334 = 0.600925216

Simplifying
v + -2.833333334 = 0.600925216

Reorder the terms:
-2.833333334 + v = 0.600925216

Solving
-2.833333334 + v = 0.600925216

Solving for variable 'v'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + v = 0.600925216 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + v = 0.600925216 + 2.833333334
v = 0.600925216 + 2.833333334

Combine like terms: 0.600925216 + 2.833333334 = 3.43425855
v = 3.43425855

Simplifying
v = 3.43425855


Subproblem 2
v + -2.833333334 = -0.600925216

Simplifying
v + -2.833333334 = -0.600925216

Reorder the terms:
-2.833333334 + v = -0.600925216

Solving
-2.833333334 + v = -0.600925216

Solving for variable 'v'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + v = -0.600925216 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + v = -0.600925216 + 2.833333334
v = -0.600925216 + 2.833333334

Combine like terms: -0.600925216 + 2.833333334 = 2.232408118
v = 2.232408118

Simplifying
v = 2.232408118


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {3.43425855, 2.232408118}

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