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Simplifying P(x) = 120x + -1x2 Multiply P * x xP = 120x + -1x2 Solving xP = 120x + -1x2 Solving for variable 'x'. Reorder the terms: -120x + xP + x2 = 120x + -1x2 + -120x + x2 Reorder the terms: -120x + xP + x2 = 120x + -120x + -1x2 + x2 Combine like terms: 120x + -120x = 0 -120x + xP + x2 = 0 + -1x2 + x2 -120x + xP + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -120x + xP + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-120 + 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 '(-120 + P + x)' equal to zero and attempt to solve: Simplifying -120 + P + x = 0 Solving -120 + P + x = 0 Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + P + 120 + x = 0 + 120 Reorder the terms: -120 + 120 + P + x = 0 + 120 Combine like terms: -120 + 120 = 0 0 + P + x = 0 + 120 P + x = 0 + 120 Combine like terms: 0 + 120 = 120 P + x = 120 Add '-1P' to each side of the equation. P + -1P + x = 120 + -1P Combine like terms: P + -1P = 0 0 + x = 120 + -1P x = 120 + -1P Simplifying x = 120 + -1PSolution
x = {0, 120 + -1P}
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