F(x)=130x-.02x^2

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Solution for F(x)=130x-.02x^2 equation: 


Simplifying
F(x) = 130x + -0.02x2

Multiply F * x
xF = 130x + -0.02x2

Solving
xF = 130x + -0.02x2

Solving for variable 'x'.

Reorder the terms:
-130x + xF + 0.02x2 = 130x + -0.02x2 + -130x + 0.02x2

Reorder the terms:
-130x + xF + 0.02x2 = 130x + -130x + -0.02x2 + 0.02x2

Combine like terms: 130x + -130x = 0
-130x + xF + 0.02x2 = 0 + -0.02x2 + 0.02x2
-130x + xF + 0.02x2 = -0.02x2 + 0.02x2

Combine like terms: -0.02x2 + 0.02x2 = 0.00
-130x + xF + 0.02x2 = 0.00

Factor out the Greatest Common Factor (GCF), 'x'.
x(-130 + F + 0.02x) = 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 '(-130 + F + 0.02x)' equal to zero and attempt to solve:

Simplifying
-130 + F + 0.02x = 0

Solving
-130 + F + 0.02x = 0

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

Add '130' to each side of the equation.
-130 + F + 130 + 0.02x = 0 + 130

Reorder the terms:
-130 + 130 + F + 0.02x = 0 + 130

Combine like terms: -130 + 130 = 0
0 + F + 0.02x = 0 + 130
F + 0.02x = 0 + 130

Combine like terms: 0 + 130 = 130
F + 0.02x = 130

Add '-1F' to each side of the equation.
F + -1F + 0.02x = 130 + -1F

Combine like terms: F + -1F = 0
0 + 0.02x = 130 + -1F
0.02x = 130 + -1F

Divide each side by '0.02'.
x = 6500 + -50F

Simplifying
x = 6500 + -50F
Solution
x = {0, 6500 + -50F}

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