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Simplifying C(x) = -0.5x2 + 60x Multiply C * x xC = -0.5x2 + 60x Reorder the terms: xC = 60x + -0.5x2 Solving xC = 60x + -0.5x2 Solving for variable 'x'. Reorder the terms: -60x + xC + 0.5x2 = 60x + -0.5x2 + -60x + 0.5x2 Reorder the terms: -60x + xC + 0.5x2 = 60x + -60x + -0.5x2 + 0.5x2 Combine like terms: 60x + -60x = 0 -60x + xC + 0.5x2 = 0 + -0.5x2 + 0.5x2 -60x + xC + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 -60x + xC + 0.5x2 = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(-60 + C + 0.5x) = 0.0Subproblem 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 '(-60 + C + 0.5x)' equal to zero and attempt to solve: Simplifying -60 + C + 0.5x = 0 Solving -60 + C + 0.5x = 0 Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + C + 60 + 0.5x = 0 + 60 Reorder the terms: -60 + 60 + C + 0.5x = 0 + 60 Combine like terms: -60 + 60 = 0 0 + C + 0.5x = 0 + 60 C + 0.5x = 0 + 60 Combine like terms: 0 + 60 = 60 C + 0.5x = 60 Add '-1C' to each side of the equation. C + -1C + 0.5x = 60 + -1C Combine like terms: C + -1C = 0 0 + 0.5x = 60 + -1C 0.5x = 60 + -1C Divide each side by '0.5'. x = 120 + -2C Simplifying x = 120 + -2CSolution
x = {0, 120 + -2C}
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