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Simplifying R(x) = 50x + -1.25x2 Multiply R * x xR = 50x + -1.25x2 Solving xR = 50x + -1.25x2 Solving for variable 'x'. Reorder the terms: -50x + xR + 1.25x2 = 50x + -1.25x2 + -50x + 1.25x2 Reorder the terms: -50x + xR + 1.25x2 = 50x + -50x + -1.25x2 + 1.25x2 Combine like terms: 50x + -50x = 0 -50x + xR + 1.25x2 = 0 + -1.25x2 + 1.25x2 -50x + xR + 1.25x2 = -1.25x2 + 1.25x2 Combine like terms: -1.25x2 + 1.25x2 = 0.00 -50x + xR + 1.25x2 = 0.00 Factor out the Greatest Common Factor (GCF), 'x'. x(-50 + R + 1.25x) = 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 '(-50 + R + 1.25x)' equal to zero and attempt to solve: Simplifying -50 + R + 1.25x = 0 Solving -50 + R + 1.25x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + R + 50 + 1.25x = 0 + 50 Reorder the terms: -50 + 50 + R + 1.25x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + R + 1.25x = 0 + 50 R + 1.25x = 0 + 50 Combine like terms: 0 + 50 = 50 R + 1.25x = 50 Add '-1R' to each side of the equation. R + -1R + 1.25x = 50 + -1R Combine like terms: R + -1R = 0 0 + 1.25x = 50 + -1R 1.25x = 50 + -1R Divide each side by '1.25'. x = 40 + -0.8R Simplifying x = 40 + -0.8RSolution
x = {0, 40 + -0.8R}
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