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Simplifying R(x) = x(85 + -2x) Multiply R * x xR = x(85 + -2x) xR = (85 * x + -2x * x) xR = (85x + -2x2) Solving xR = 85x + -2x2 Solving for variable 'x'. Reorder the terms: -85x + xR + 2x2 = 85x + -2x2 + -85x + 2x2 Reorder the terms: -85x + xR + 2x2 = 85x + -85x + -2x2 + 2x2 Combine like terms: 85x + -85x = 0 -85x + xR + 2x2 = 0 + -2x2 + 2x2 -85x + xR + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -85x + xR + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-85 + R + 2x) = 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 '(-85 + R + 2x)' equal to zero and attempt to solve: Simplifying -85 + R + 2x = 0 Solving -85 + R + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + R + 85 + 2x = 0 + 85 Reorder the terms: -85 + 85 + R + 2x = 0 + 85 Combine like terms: -85 + 85 = 0 0 + R + 2x = 0 + 85 R + 2x = 0 + 85 Combine like terms: 0 + 85 = 85 R + 2x = 85 Add '-1R' to each side of the equation. R + -1R + 2x = 85 + -1R Combine like terms: R + -1R = 0 0 + 2x = 85 + -1R 2x = 85 + -1R Divide each side by '2'. x = 42.5 + -0.5R Simplifying x = 42.5 + -0.5RSolution
x = {0, 42.5 + -0.5R}
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