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Simplifying R(x) = -0.05x2 + 300x Multiply R * x xR = -0.05x2 + 300x Reorder the terms: xR = 300x + -0.05x2 Solving xR = 300x + -0.05x2 Solving for variable 'x'. Reorder the terms: -300x + xR + 0.05x2 = 300x + -0.05x2 + -300x + 0.05x2 Reorder the terms: -300x + xR + 0.05x2 = 300x + -300x + -0.05x2 + 0.05x2 Combine like terms: 300x + -300x = 0 -300x + xR + 0.05x2 = 0 + -0.05x2 + 0.05x2 -300x + xR + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -300x + xR + 0.05x2 = 0.00 Factor out the Greatest Common Factor (GCF), 'x'. x(-300 + R + 0.05x) = 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 '(-300 + R + 0.05x)' equal to zero and attempt to solve: Simplifying -300 + R + 0.05x = 0 Solving -300 + R + 0.05x = 0 Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + R + 300 + 0.05x = 0 + 300 Reorder the terms: -300 + 300 + R + 0.05x = 0 + 300 Combine like terms: -300 + 300 = 0 0 + R + 0.05x = 0 + 300 R + 0.05x = 0 + 300 Combine like terms: 0 + 300 = 300 R + 0.05x = 300 Add '-1R' to each side of the equation. R + -1R + 0.05x = 300 + -1R Combine like terms: R + -1R = 0 0 + 0.05x = 300 + -1R 0.05x = 300 + -1R Divide each side by '0.05'. x = 6000 + -20R Simplifying x = 6000 + -20RSolution
x = {0, 6000 + -20R}
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