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Simplifying 9000 = p(1200 + -30p) 9000 = (1200 * p + -30p * p) 9000 = (1200p + -30p2) Solving 9000 = 1200p + -30p2 Solving for variable 'p'. Reorder the terms: 9000 + -1200p + 30p2 = 1200p + -1200p + -30p2 + 30p2 Combine like terms: 1200p + -1200p = 0 9000 + -1200p + 30p2 = 0 + -30p2 + 30p2 9000 + -1200p + 30p2 = -30p2 + 30p2 Combine like terms: -30p2 + 30p2 = 0 9000 + -1200p + 30p2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(300 + -40p + p2) = 0 Factor a trinomial. 30((10 + -1p)(30 + -1p)) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(10 + -1p)' equal to zero and attempt to solve: Simplifying 10 + -1p = 0 Solving 10 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1p = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1p = 0 + -10 -1p = 0 + -10 Combine like terms: 0 + -10 = -10 -1p = -10 Divide each side by '-1'. p = 10 Simplifying p = 10Subproblem 2
Set the factor '(30 + -1p)' equal to zero and attempt to solve: Simplifying 30 + -1p = 0 Solving 30 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1p = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1p = 0 + -30 -1p = 0 + -30 Combine like terms: 0 + -30 = -30 -1p = -30 Divide each side by '-1'. p = 30 Simplifying p = 30Solution
p = {10, 30}
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