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Simplifying P(x) = -25x2 + 300x Multiply P * x xP = -25x2 + 300x Reorder the terms: xP = 300x + -25x2 Solving xP = 300x + -25x2 Solving for variable 'x'. Reorder the terms: -300x + xP + 25x2 = 300x + -25x2 + -300x + 25x2 Reorder the terms: -300x + xP + 25x2 = 300x + -300x + -25x2 + 25x2 Combine like terms: 300x + -300x = 0 -300x + xP + 25x2 = 0 + -25x2 + 25x2 -300x + xP + 25x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 -300x + xP + 25x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-300 + P + 25x) = 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 '(-300 + P + 25x)' equal to zero and attempt to solve: Simplifying -300 + P + 25x = 0 Solving -300 + P + 25x = 0 Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + P + 300 + 25x = 0 + 300 Reorder the terms: -300 + 300 + P + 25x = 0 + 300 Combine like terms: -300 + 300 = 0 0 + P + 25x = 0 + 300 P + 25x = 0 + 300 Combine like terms: 0 + 300 = 300 P + 25x = 300 Add '-1P' to each side of the equation. P + -1P + 25x = 300 + -1P Combine like terms: P + -1P = 0 0 + 25x = 300 + -1P 25x = 300 + -1P Divide each side by '25'. x = 12 + -0.04P Simplifying x = 12 + -0.04PSolution
x = {0, 12 + -0.04P}
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