R(x)=-2.5x^2+500x

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Solution for R(x)=-2.5x^2+500x equation: 


Simplifying
R(x) = -2.5x2 + 500x

Multiply R * x
xR = -2.5x2 + 500x

Reorder the terms:
xR = 500x + -2.5x2

Solving
xR = 500x + -2.5x2

Solving for variable 'x'.

Reorder the terms:
-500x + xR + 2.5x2 = 500x + -2.5x2 + -500x + 2.5x2

Reorder the terms:
-500x + xR + 2.5x2 = 500x + -500x + -2.5x2 + 2.5x2

Combine like terms: 500x + -500x = 0
-500x + xR + 2.5x2 = 0 + -2.5x2 + 2.5x2
-500x + xR + 2.5x2 = -2.5x2 + 2.5x2

Combine like terms: -2.5x2 + 2.5x2 = 0.0
-500x + xR + 2.5x2 = 0.0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-500 + R + 2.5x) = 0.0


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 '(-500 + R + 2.5x)' equal to zero and attempt to solve:

Simplifying
-500 + R + 2.5x = 0

Solving
-500 + R + 2.5x = 0

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

Add '500' to each side of the equation.
-500 + R + 500 + 2.5x = 0 + 500

Reorder the terms:
-500 + 500 + R + 2.5x = 0 + 500

Combine like terms: -500 + 500 = 0
0 + R + 2.5x = 0 + 500
R + 2.5x = 0 + 500

Combine like terms: 0 + 500 = 500
R + 2.5x = 500

Add '-1R' to each side of the equation.
R + -1R + 2.5x = 500 + -1R

Combine like terms: R + -1R = 0
0 + 2.5x = 500 + -1R
2.5x = 500 + -1R

Divide each side by '2.5'.
x = 200 + -0.4R

Simplifying
x = 200 + -0.4R
Solution
x = {0, 200 + -0.4R}

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