R(x)=-0.02x^2+24x

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Solution for R(x)=-0.02x^2+24x equation:


Simplifying
R(x) = -0.02x2 + 24x

Multiply R * x
xR = -0.02x2 + 24x

Reorder the terms:
xR = 24x + -0.02x2

Solving
xR = 24x + -0.02x2

Solving for variable 'x'.

Reorder the terms:
-24x + xR + 0.02x2 = 24x + -0.02x2 + -24x + 0.02x2

Reorder the terms:
-24x + xR + 0.02x2 = 24x + -24x + -0.02x2 + 0.02x2

Combine like terms: 24x + -24x = 0
-24x + xR + 0.02x2 = 0 + -0.02x2 + 0.02x2
-24x + xR + 0.02x2 = -0.02x2 + 0.02x2

Combine like terms: -0.02x2 + 0.02x2 = 0.00
-24x + xR + 0.02x2 = 0.00

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + R + 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 '(-24 + R + 0.02x)' equal to zero and attempt to solve: Simplifying -24 + R + 0.02x = 0 Solving -24 + R + 0.02x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + R + 24 + 0.02x = 0 + 24 Reorder the terms: -24 + 24 + R + 0.02x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + R + 0.02x = 0 + 24 R + 0.02x = 0 + 24 Combine like terms: 0 + 24 = 24 R + 0.02x = 24 Add '-1R' to each side of the equation. R + -1R + 0.02x = 24 + -1R Combine like terms: R + -1R = 0 0 + 0.02x = 24 + -1R 0.02x = 24 + -1R Divide each side by '0.02'. x = 1200 + -50R Simplifying x = 1200 + -50R

Solution

x = {0, 1200 + -50R}

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