200=.05v^2+2.2v

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Solution for 200=.05v^2+2.2v equation:


Simplifying
200 = 0.05v2 + 2.2v

Reorder the terms:
200 = 2.2v + 0.05v2

Solving
200 = 2.2v + 0.05v2

Solving for variable 'v'.

Reorder the terms:
200 + -2.2v + -0.05v2 = 2.2v + -2.2v + 0.05v2 + -0.05v2

Combine like terms: 2.2v + -2.2v = 0.0
200 + -2.2v + -0.05v2 = 0.0 + 0.05v2 + -0.05v2
200 + -2.2v + -0.05v2 = 0.05v2 + -0.05v2

Combine like terms: 0.05v2 + -0.05v2 = 0.00
200 + -2.2v + -0.05v2 = 0.00

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
-4000 + 44v + v2 = 0

Move the constant term to the right:

Add '4000' to each side of the equation.
-4000 + 44v + 4000 + v2 = 0 + 4000

Reorder the terms:
-4000 + 4000 + 44v + v2 = 0 + 4000

Combine like terms: -4000 + 4000 = 0
0 + 44v + v2 = 0 + 4000
44v + v2 = 0 + 4000

Combine like terms: 0 + 4000 = 4000
44v + v2 = 4000

The v term is 44v.  Take half its coefficient (22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
44v + 484 + v2 = 4000 + 484

Reorder the terms:
484 + 44v + v2 = 4000 + 484

Combine like terms: 4000 + 484 = 4484
484 + 44v + v2 = 4484

Factor a perfect square on the left side:
(v + 22)(v + 22) = 4484

Calculate the square root of the right side: 66.962676171

Break this problem into two subproblems by setting 
(v + 22) equal to 66.962676171 and -66.962676171.

Subproblem 1

v + 22 = 66.962676171 Simplifying v + 22 = 66.962676171 Reorder the terms: 22 + v = 66.962676171 Solving 22 + v = 66.962676171 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + v = 66.962676171 + -22 Combine like terms: 22 + -22 = 0 0 + v = 66.962676171 + -22 v = 66.962676171 + -22 Combine like terms: 66.962676171 + -22 = 44.962676171 v = 44.962676171 Simplifying v = 44.962676171

Subproblem 2

v + 22 = -66.962676171 Simplifying v + 22 = -66.962676171 Reorder the terms: 22 + v = -66.962676171 Solving 22 + v = -66.962676171 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + v = -66.962676171 + -22 Combine like terms: 22 + -22 = 0 0 + v = -66.962676171 + -22 v = -66.962676171 + -22 Combine like terms: -66.962676171 + -22 = -88.962676171 v = -88.962676171 Simplifying v = -88.962676171

Solution

The solution to the problem is based on the solutions from the subproblems. v = {44.962676171, -88.962676171}

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