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Simplifying R(x) = -0.1x2 + 500x Multiply R * x xR = -0.1x2 + 500x Reorder the terms: xR = 500x + -0.1x2 Solving xR = 500x + -0.1x2 Solving for variable 'x'. Reorder the terms: -500x + xR + 0.1x2 = 500x + -0.1x2 + -500x + 0.1x2 Reorder the terms: -500x + xR + 0.1x2 = 500x + -500x + -0.1x2 + 0.1x2 Combine like terms: 500x + -500x = 0 -500x + xR + 0.1x2 = 0 + -0.1x2 + 0.1x2 -500x + xR + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -500x + xR + 0.1x2 = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(-500 + R + 0.1x) = 0.0Subproblem 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 = 0Subproblem 2
Set the factor '(-500 + R + 0.1x)' equal to zero and attempt to solve: Simplifying -500 + R + 0.1x = 0 Solving -500 + R + 0.1x = 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 + 0.1x = 0 + 500 Reorder the terms: -500 + 500 + R + 0.1x = 0 + 500 Combine like terms: -500 + 500 = 0 0 + R + 0.1x = 0 + 500 R + 0.1x = 0 + 500 Combine like terms: 0 + 500 = 500 R + 0.1x = 500 Add '-1R' to each side of the equation. R + -1R + 0.1x = 500 + -1R Combine like terms: R + -1R = 0 0 + 0.1x = 500 + -1R 0.1x = 500 + -1R Divide each side by '0.1'. x = 5000 + -10R Simplifying x = 5000 + -10RSolution
x = {0, 5000 + -10R}
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