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Simplifying P(x) = -75x2 + 15000x Multiply P * x xP = -75x2 + 15000x Reorder the terms: xP = 15000x + -75x2 Solving xP = 15000x + -75x2 Solving for variable 'x'. Reorder the terms: -15000x + xP + 75x2 = 15000x + -75x2 + -15000x + 75x2 Reorder the terms: -15000x + xP + 75x2 = 15000x + -15000x + -75x2 + 75x2 Combine like terms: 15000x + -15000x = 0 -15000x + xP + 75x2 = 0 + -75x2 + 75x2 -15000x + xP + 75x2 = -75x2 + 75x2 Combine like terms: -75x2 + 75x2 = 0 -15000x + xP + 75x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-15000 + P + 75x) = 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 '(-15000 + P + 75x)' equal to zero and attempt to solve: Simplifying -15000 + P + 75x = 0 Solving -15000 + P + 75x = 0 Move all terms containing x to the left, all other terms to the right. Add '15000' to each side of the equation. -15000 + P + 15000 + 75x = 0 + 15000 Reorder the terms: -15000 + 15000 + P + 75x = 0 + 15000 Combine like terms: -15000 + 15000 = 0 0 + P + 75x = 0 + 15000 P + 75x = 0 + 15000 Combine like terms: 0 + 15000 = 15000 P + 75x = 15000 Add '-1P' to each side of the equation. P + -1P + 75x = 15000 + -1P Combine like terms: P + -1P = 0 0 + 75x = 15000 + -1P 75x = 15000 + -1P Divide each side by '75'. x = 200 + -0.01333333333P Simplifying x = 200 + -0.01333333333PSolution
x = {0, 200 + -0.01333333333P}
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