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Simplifying P(x) = 40x + -0.25x2 Multiply P * x xP = 40x + -0.25x2 Solving xP = 40x + -0.25x2 Solving for variable 'x'. Reorder the terms: -40x + xP + 0.25x2 = 40x + -0.25x2 + -40x + 0.25x2 Reorder the terms: -40x + xP + 0.25x2 = 40x + -40x + -0.25x2 + 0.25x2 Combine like terms: 40x + -40x = 0 -40x + xP + 0.25x2 = 0 + -0.25x2 + 0.25x2 -40x + xP + 0.25x2 = -0.25x2 + 0.25x2 Combine like terms: -0.25x2 + 0.25x2 = 0.00 -40x + xP + 0.25x2 = 0.00 Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + P + 0.25x) = 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 '(-40 + P + 0.25x)' equal to zero and attempt to solve: Simplifying -40 + P + 0.25x = 0 Solving -40 + P + 0.25x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + P + 40 + 0.25x = 0 + 40 Reorder the terms: -40 + 40 + P + 0.25x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + P + 0.25x = 0 + 40 P + 0.25x = 0 + 40 Combine like terms: 0 + 40 = 40 P + 0.25x = 40 Add '-1P' to each side of the equation. P + -1P + 0.25x = 40 + -1P Combine like terms: P + -1P = 0 0 + 0.25x = 40 + -1P 0.25x = 40 + -1P Divide each side by '0.25'. x = 160 + -4P Simplifying x = 160 + -4PSolution
x = {0, 160 + -4P}
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