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