10.6=1.6+0.03v+0.003v^2

Solution for 10.6=1.6+0.03v+0.003v^2 equation:

Simplifying
10.6 = 1.6 + 0.03v + 0.003v2

Solving
10.6 = 1.6 + 0.03v + 0.003v2

Solving for variable 'v'.

Combine like terms: 10.6 + -1.6 = 9
9 + -0.03v + -0.003v2 = 1.6 + 0.03v + 0.003v2 + -1.6 + -0.03v + -0.003v2

Reorder the terms:
9 + -0.03v + -0.003v2 = 1.6 + -1.6 + 0.03v + -0.03v + 0.003v2 + -0.003v2

Combine like terms: 1.6 + -1.6 = 0.0
9 + -0.03v + -0.003v2 = 0.0 + 0.03v + -0.03v + 0.003v2 + -0.003v2
9 + -0.03v + -0.003v2 = 0.03v + -0.03v + 0.003v2 + -0.003v2

Combine like terms: 0.03v + -0.03v = 0.00
9 + -0.03v + -0.003v2 = 0.00 + 0.003v2 + -0.003v2
9 + -0.03v + -0.003v2 = 0.003v2 + -0.003v2

Combine like terms: 0.003v2 + -0.003v2 = 0.000
9 + -0.03v + -0.003v2 = 0.000

Begin completing the square.  Divide all terms by
-0.003 the coefficient of the squared term: 

Divide each side by '-0.003'.
-3000 + 10v + v2 = 0

Move the constant term to the right:

Add '3000' to each side of the equation.
-3000 + 10v + 3000 + v2 = 0 + 3000

Reorder the terms:
-3000 + 3000 + 10v + v2 = 0 + 3000

Combine like terms: -3000 + 3000 = 0
0 + 10v + v2 = 0 + 3000
10v + v2 = 0 + 3000

Combine like terms: 0 + 3000 = 3000
10v + v2 = 3000

The v term is 10v.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10v + 25 + v2 = 3000 + 25

Reorder the terms:
25 + 10v + v2 = 3000 + 25

Combine like terms: 3000 + 25 = 3025
25 + 10v + v2 = 3025

Factor a perfect square on the left side:
(v + 5)(v + 5) = 3025

Calculate the square root of the right side: 55

Break this problem into two subproblems by setting 
(v + 5) equal to 55 and -55.

Subproblem 1
v + 5 = 55

Simplifying
v + 5 = 55

Reorder the terms:
5 + v = 55

Solving
5 + v = 55

Solving for variable 'v'.

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

Add '-5' to each side of the equation.
5 + -5 + v = 55 + -5

Combine like terms: 5 + -5 = 0
0 + v = 55 + -5
v = 55 + -5

Combine like terms: 55 + -5 = 50
v = 50

Simplifying
v = 50

Subproblem 2
v + 5 = -55

Simplifying
v + 5 = -55

Reorder the terms:
5 + v = -55

Solving
5 + v = -55

Solving for variable 'v'.

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

Add '-5' to each side of the equation.
5 + -5 + v = -55 + -5

Combine like terms: 5 + -5 = 0
0 + v = -55 + -5
v = -55 + -5

Combine like terms: -55 + -5 = -60
v = -60

Simplifying
v = -60

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {50, -60}