15=0.002(2v^2+10v+3000)

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Solution for 15=0.002(2v^2+10v+3000) equation: 


Simplifying
15 = 0.002(2v2 + 10v + 3000)

Reorder the terms:
15 = 0.002(3000 + 10v + 2v2)
15 = (3000 * 0.002 + 10v * 0.002 + 2v2 * 0.002)
15 = (6 + 0.02v + 0.004v2)

Solving
15 = 6 + 0.02v + 0.004v2

Solving for variable 'v'.

Combine like terms: 15 + -6 = 9
9 + -0.02v + -0.004v2 = 6 + 0.02v + 0.004v2 + -6 + -0.02v + -0.004v2

Reorder the terms:
9 + -0.02v + -0.004v2 = 6 + -6 + 0.02v + -0.02v + 0.004v2 + -0.004v2

Combine like terms: 6 + -6 = 0
9 + -0.02v + -0.004v2 = 0 + 0.02v + -0.02v + 0.004v2 + -0.004v2
9 + -0.02v + -0.004v2 = 0.02v + -0.02v + 0.004v2 + -0.004v2

Combine like terms: 0.02v + -0.02v = 0.00
9 + -0.02v + -0.004v2 = 0.00 + 0.004v2 + -0.004v2
9 + -0.02v + -0.004v2 = 0.004v2 + -0.004v2

Combine like terms: 0.004v2 + -0.004v2 = 0.000
9 + -0.02v + -0.004v2 = 0.000

Begin completing the square.  Divide all terms by
-0.004 the coefficient of the squared term: 

Divide each side by '-0.004'.
-2250 + 5v + v2 = 0

Move the constant term to the right:

Add '2250' to each side of the equation.
-2250 + 5v + 2250 + v2 = 0 + 2250

Reorder the terms:
-2250 + 2250 + 5v + v2 = 0 + 2250

Combine like terms: -2250 + 2250 = 0
0 + 5v + v2 = 0 + 2250
5v + v2 = 0 + 2250

Combine like terms: 0 + 2250 = 2250
5v + v2 = 2250

The v term is 5v.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5v + 6.25 + v2 = 2250 + 6.25

Reorder the terms:
6.25 + 5v + v2 = 2250 + 6.25

Combine like terms: 2250 + 6.25 = 2256.25
6.25 + 5v + v2 = 2256.25

Factor a perfect square on the left side:
(v + 2.5)(v + 2.5) = 2256.25

Calculate the square root of the right side: 47.5

Break this problem into two subproblems by setting 
(v + 2.5) equal to 47.5 and -47.5.


Subproblem 1
v + 2.5 = 47.5

Simplifying
v + 2.5 = 47.5

Reorder the terms:
2.5 + v = 47.5

Solving
2.5 + v = 47.5

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = 47.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = 47.5 + -2.5
v = 47.5 + -2.5

Combine like terms: 47.5 + -2.5 = 45
v = 45

Simplifying
v = 45


Subproblem 2
v + 2.5 = -47.5

Simplifying
v + 2.5 = -47.5

Reorder the terms:
2.5 + v = -47.5

Solving
2.5 + v = -47.5

Solving for variable 'v'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + v = -47.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + v = -47.5 + -2.5
v = -47.5 + -2.5

Combine like terms: -47.5 + -2.5 = -50
v = -50

Simplifying
v = -50


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {45, -50}

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