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Simplifying R(x) = 5x + -0.04x2 Multiply R * x xR = 5x + -0.04x2 Solving xR = 5x + -0.04x2 Solving for variable 'x'. Reorder the terms: -5x + xR + 0.04x2 = 5x + -0.04x2 + -5x + 0.04x2 Reorder the terms: -5x + xR + 0.04x2 = 5x + -5x + -0.04x2 + 0.04x2 Combine like terms: 5x + -5x = 0 -5x + xR + 0.04x2 = 0 + -0.04x2 + 0.04x2 -5x + xR + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 -5x + xR + 0.04x2 = 0.00 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + R + 0.04x) = 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 '(-5 + R + 0.04x)' equal to zero and attempt to solve: Simplifying -5 + R + 0.04x = 0 Solving -5 + R + 0.04x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + R + 5 + 0.04x = 0 + 5 Reorder the terms: -5 + 5 + R + 0.04x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + R + 0.04x = 0 + 5 R + 0.04x = 0 + 5 Combine like terms: 0 + 5 = 5 R + 0.04x = 5 Add '-1R' to each side of the equation. R + -1R + 0.04x = 5 + -1R Combine like terms: R + -1R = 0 0 + 0.04x = 5 + -1R 0.04x = 5 + -1R Divide each side by '0.04'. x = 125 + -25R Simplifying x = 125 + -25RSolution
x = {0, 125 + -25R}
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