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

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


Simplifying
R(x) = 200x + -2x2

Multiply R * x
xR = 200x + -2x2

Solving
xR = 200x + -2x2

Solving for variable 'x'.

Reorder the terms:
-200x + xR + 2x2 = 200x + -2x2 + -200x + 2x2

Reorder the terms:
-200x + xR + 2x2 = 200x + -200x + -2x2 + 2x2

Combine like terms: 200x + -200x = 0
-200x + xR + 2x2 = 0 + -2x2 + 2x2
-200x + xR + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-200x + xR + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-200 + R + 2x) = 0

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 + 2x)' equal to zero and attempt to solve: Simplifying -200 + R + 2x = 0 Solving -200 + R + 2x = 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 + 2x = 0 + 200 Reorder the terms: -200 + 200 + R + 2x = 0 + 200 Combine like terms: -200 + 200 = 0 0 + R + 2x = 0 + 200 R + 2x = 0 + 200 Combine like terms: 0 + 200 = 200 R + 2x = 200 Add '-1R' to each side of the equation. R + -1R + 2x = 200 + -1R Combine like terms: R + -1R = 0 0 + 2x = 200 + -1R 2x = 200 + -1R Divide each side by '2'. x = 100 + -0.5R Simplifying x = 100 + -0.5R

Solution

x = {0, 100 + -0.5R}

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