200=1.1v+.06v^2

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Solution for 200=1.1v+.06v^2 equation: 


Simplifying
200 = 1.1v + 0.06v2

Solving
200 = 1.1v + 0.06v2

Solving for variable 'v'.

Reorder the terms:
200 + -1.1v + -0.06v2 = 1.1v + -1.1v + 0.06v2 + -0.06v2

Combine like terms: 1.1v + -1.1v = 0.0
200 + -1.1v + -0.06v2 = 0.0 + 0.06v2 + -0.06v2
200 + -1.1v + -0.06v2 = 0.06v2 + -0.06v2

Combine like terms: 0.06v2 + -0.06v2 = 0.00
200 + -1.1v + -0.06v2 = 0.00

Begin completing the square.  Divide all terms by
-0.06 the coefficient of the squared term: 

Divide each side by '-0.06'.
-3333.333333 + 18.33333333v + v2 = 0

Move the constant term to the right:

Add '3333.333333' to each side of the equation.
-3333.333333 + 18.33333333v + 3333.333333 + v2 = 0 + 3333.333333

Reorder the terms:
-3333.333333 + 3333.333333 + 18.33333333v + v2 = 0 + 3333.333333

Combine like terms: -3333.333333 + 3333.333333 = 0.000000
0.000000 + 18.33333333v + v2 = 0 + 3333.333333
18.33333333v + v2 = 0 + 3333.333333

Combine like terms: 0 + 3333.333333 = 3333.333333
18.33333333v + v2 = 3333.333333

The v term is 18.33333333v.  Take half its coefficient (9.166666665).
Square it (84.02777775) and add it to both sides.

Add '84.02777775' to each side of the equation.
18.33333333v + 84.02777775 + v2 = 3333.333333 + 84.02777775

Reorder the terms:
84.02777775 + 18.33333333v + v2 = 3333.333333 + 84.02777775

Combine like terms: 3333.333333 + 84.02777775 = 3417.36111075
84.02777775 + 18.33333333v + v2 = 3417.36111075

Factor a perfect square on the left side:
(v + 9.166666665)(v + 9.166666665) = 3417.36111075

Calculate the square root of the right side: 58.458199688

Break this problem into two subproblems by setting 
(v + 9.166666665) equal to 58.458199688 and -58.458199688.


Subproblem 1
v + 9.166666665 = 58.458199688

Simplifying
v + 9.166666665 = 58.458199688

Reorder the terms:
9.166666665 + v = 58.458199688

Solving
9.166666665 + v = 58.458199688

Solving for variable 'v'.

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

Add '-9.166666665' to each side of the equation.
9.166666665 + -9.166666665 + v = 58.458199688 + -9.166666665

Combine like terms: 9.166666665 + -9.166666665 = 0.000000000
0.000000000 + v = 58.458199688 + -9.166666665
v = 58.458199688 + -9.166666665

Combine like terms: 58.458199688 + -9.166666665 = 49.291533023
v = 49.291533023

Simplifying
v = 49.291533023


Subproblem 2
v + 9.166666665 = -58.458199688

Simplifying
v + 9.166666665 = -58.458199688

Reorder the terms:
9.166666665 + v = -58.458199688

Solving
9.166666665 + v = -58.458199688

Solving for variable 'v'.

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

Add '-9.166666665' to each side of the equation.
9.166666665 + -9.166666665 + v = -58.458199688 + -9.166666665

Combine like terms: 9.166666665 + -9.166666665 = 0.000000000
0.000000000 + v = -58.458199688 + -9.166666665
v = -58.458199688 + -9.166666665

Combine like terms: -58.458199688 + -9.166666665 = -67.624866353
v = -67.624866353

Simplifying
v = -67.624866353


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {49.291533023, -67.624866353}

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