R(x)=150x-.05x^2

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Solution for R(x)=150x-.05x^2 equation: 


Simplifying
R(x) = 150x + -0.05x2

Multiply R * x
xR = 150x + -0.05x2

Solving
xR = 150x + -0.05x2

Solving for variable 'x'.

Reorder the terms:
-150x + xR + 0.05x2 = 150x + -0.05x2 + -150x + 0.05x2

Reorder the terms:
-150x + xR + 0.05x2 = 150x + -150x + -0.05x2 + 0.05x2

Combine like terms: 150x + -150x = 0
-150x + xR + 0.05x2 = 0 + -0.05x2 + 0.05x2
-150x + xR + 0.05x2 = -0.05x2 + 0.05x2

Combine like terms: -0.05x2 + 0.05x2 = 0.00
-150x + xR + 0.05x2 = 0.00

Factor out the Greatest Common Factor (GCF), 'x'.
x(-150 + R + 0.05x) = 0.00


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 '(-150 + R + 0.05x)' equal to zero and attempt to solve:

Simplifying
-150 + R + 0.05x = 0

Solving
-150 + R + 0.05x = 0

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

Add '150' to each side of the equation.
-150 + R + 150 + 0.05x = 0 + 150

Reorder the terms:
-150 + 150 + R + 0.05x = 0 + 150

Combine like terms: -150 + 150 = 0
0 + R + 0.05x = 0 + 150
R + 0.05x = 0 + 150

Combine like terms: 0 + 150 = 150
R + 0.05x = 150

Add '-1R' to each side of the equation.
R + -1R + 0.05x = 150 + -1R

Combine like terms: R + -1R = 0
0 + 0.05x = 150 + -1R
0.05x = 150 + -1R

Divide each side by '0.05'.
x = 3000 + -20R

Simplifying
x = 3000 + -20R
Solution
x = {0, 3000 + -20R}

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