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Simplifying R(x) = 3x + -0.01x2 Multiply R * x xR = 3x + -0.01x2 Solving xR = 3x + -0.01x2 Solving for variable 'x'. Reorder the terms: -3x + xR + 0.01x2 = 3x + -0.01x2 + -3x + 0.01x2 Reorder the terms: -3x + xR + 0.01x2 = 3x + -3x + -0.01x2 + 0.01x2 Combine like terms: 3x + -3x = 0 -3x + xR + 0.01x2 = 0 + -0.01x2 + 0.01x2 -3x + xR + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -3x + xR + 0.01x2 = 0.00 Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + R + 0.01x) = 0.00Subproblem 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 '(-3 + R + 0.01x)' equal to zero and attempt to solve: Simplifying -3 + R + 0.01x = 0 Solving -3 + R + 0.01x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + R + 3 + 0.01x = 0 + 3 Reorder the terms: -3 + 3 + R + 0.01x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + R + 0.01x = 0 + 3 R + 0.01x = 0 + 3 Combine like terms: 0 + 3 = 3 R + 0.01x = 3 Add '-1R' to each side of the equation. R + -1R + 0.01x = 3 + -1R Combine like terms: R + -1R = 0 0 + 0.01x = 3 + -1R 0.01x = 3 + -1R Divide each side by '0.01'. x = 300 + -100R Simplifying x = 300 + -100RSolution
x = {0, 300 + -100R}
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