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Simplifying P(x) = -1x2 + 50x Multiply P * x xP = -1x2 + 50x Reorder the terms: xP = 50x + -1x2 Solving xP = 50x + -1x2 Solving for variable 'x'. Reorder the terms: -50x + xP + x2 = 50x + -1x2 + -50x + x2 Reorder the terms: -50x + xP + x2 = 50x + -50x + -1x2 + x2 Combine like terms: 50x + -50x = 0 -50x + xP + x2 = 0 + -1x2 + x2 -50x + xP + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -50x + xP + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-50 + P + x) = 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 '(-50 + P + x)' equal to zero and attempt to solve: Simplifying -50 + P + x = 0 Solving -50 + P + x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + P + 50 + x = 0 + 50 Reorder the terms: -50 + 50 + P + x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + P + x = 0 + 50 P + x = 0 + 50 Combine like terms: 0 + 50 = 50 P + x = 50 Add '-1P' to each side of the equation. P + -1P + x = 50 + -1P Combine like terms: P + -1P = 0 0 + x = 50 + -1P x = 50 + -1P Simplifying x = 50 + -1PSolution
x = {0, 50 + -1P}
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