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Simplifying P(x) = 0.0025x2 + 1.075x Multiply P * x xP = 0.0025x2 + 1.075x Reorder the terms: xP = 1.075x + 0.0025x2 Solving xP = 1.075x + 0.0025x2 Solving for variable 'x'. Reorder the terms: -1.075x + xP + -0.0025x2 = 1.075x + 0.0025x2 + -1.075x + -0.0025x2 Reorder the terms: -1.075x + xP + -0.0025x2 = 1.075x + -1.075x + 0.0025x2 + -0.0025x2 Combine like terms: 1.075x + -1.075x = 0.000 -1.075x + xP + -0.0025x2 = 0.000 + 0.0025x2 + -0.0025x2 -1.075x + xP + -0.0025x2 = 0.0025x2 + -0.0025x2 Combine like terms: 0.0025x2 + -0.0025x2 = 0.0000 -1.075x + xP + -0.0025x2 = 0.0000 Factor out the Greatest Common Factor (GCF), 'x'. x(-1.075 + P + -0.0025x) = 0.0000Subproblem 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 '(-1.075 + P + -0.0025x)' equal to zero and attempt to solve: Simplifying -1.075 + P + -0.0025x = 0 Solving -1.075 + P + -0.0025x = 0 Move all terms containing x to the left, all other terms to the right. Add '1.075' to each side of the equation. -1.075 + P + 1.075 + -0.0025x = 0 + 1.075 Reorder the terms: -1.075 + 1.075 + P + -0.0025x = 0 + 1.075 Combine like terms: -1.075 + 1.075 = 0.000 0.000 + P + -0.0025x = 0 + 1.075 P + -0.0025x = 0 + 1.075 Combine like terms: 0 + 1.075 = 1.075 P + -0.0025x = 1.075 Add '-1P' to each side of the equation. P + -1P + -0.0025x = 1.075 + -1P Combine like terms: P + -1P = 0 0 + -0.0025x = 1.075 + -1P -0.0025x = 1.075 + -1P Divide each side by '-0.0025'. x = -430 + 400P Simplifying x = -430 + 400PSolution
x = {0, -430 + 400P}
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