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Simplifying R(x) = -3x2 + 75x Multiply R * x xR = -3x2 + 75x Reorder the terms: xR = 75x + -3x2 Solving xR = 75x + -3x2 Solving for variable 'x'. Reorder the terms: -75x + xR + 3x2 = 75x + -3x2 + -75x + 3x2 Reorder the terms: -75x + xR + 3x2 = 75x + -75x + -3x2 + 3x2 Combine like terms: 75x + -75x = 0 -75x + xR + 3x2 = 0 + -3x2 + 3x2 -75x + xR + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -75x + xR + 3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-75 + R + 3x) = 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 '(-75 + R + 3x)' equal to zero and attempt to solve: Simplifying -75 + R + 3x = 0 Solving -75 + R + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + R + 75 + 3x = 0 + 75 Reorder the terms: -75 + 75 + R + 3x = 0 + 75 Combine like terms: -75 + 75 = 0 0 + R + 3x = 0 + 75 R + 3x = 0 + 75 Combine like terms: 0 + 75 = 75 R + 3x = 75 Add '-1R' to each side of the equation. R + -1R + 3x = 75 + -1R Combine like terms: R + -1R = 0 0 + 3x = 75 + -1R 3x = 75 + -1R Divide each side by '3'. x = 25 + -0.3333333333R Simplifying x = 25 + -0.3333333333RSolution
x = {0, 25 + -0.3333333333R}
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