R(x)=200x-0.0002x^2

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Solution for R(x)=200x-0.0002x^2 equation: 


Simplifying
R(x) = 200x + -0.0002x2

Multiply R * x
xR = 200x + -0.0002x2

Solving
xR = 200x + -0.0002x2

Solving for variable 'x'.

Reorder the terms:
-200x + xR + 0.0002x2 = 200x + -0.0002x2 + -200x + 0.0002x2

Reorder the terms:
-200x + xR + 0.0002x2 = 200x + -200x + -0.0002x2 + 0.0002x2

Combine like terms: 200x + -200x = 0
-200x + xR + 0.0002x2 = 0 + -0.0002x2 + 0.0002x2
-200x + xR + 0.0002x2 = -0.0002x2 + 0.0002x2

Combine like terms: -0.0002x2 + 0.0002x2 = 0.0000
-200x + xR + 0.0002x2 = 0.0000

Factor out the Greatest Common Factor (GCF), 'x'.
x(-200 + R + 0.0002x) = 0.0000


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-200 + R + 0.0002x)' equal to zero and attempt to solve:

Simplifying
-200 + R + 0.0002x = 0

Solving
-200 + R + 0.0002x = 0

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

Add '200' to each side of the equation.
-200 + R + 200 + 0.0002x = 0 + 200

Reorder the terms:
-200 + 200 + R + 0.0002x = 0 + 200

Combine like terms: -200 + 200 = 0
0 + R + 0.0002x = 0 + 200
R + 0.0002x = 0 + 200

Combine like terms: 0 + 200 = 200
R + 0.0002x = 200

Add '-1R' to each side of the equation.
R + -1R + 0.0002x = 200 + -1R

Combine like terms: R + -1R = 0
0 + 0.0002x = 200 + -1R
0.0002x = 200 + -1R

Divide each side by '0.0002'.
x = 1000000 + -5000R

Simplifying
x = 1000000 + -5000R
Solution
x = {0, 1000000 + -5000R}

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