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Simplifying 5000 = -1p2 + 120p + 1400 Reorder the terms: 5000 = 1400 + 120p + -1p2 Solving 5000 = 1400 + 120p + -1p2 Solving for variable 'p'. Combine like terms: 5000 + -1400 = 3600 3600 + -120p + p2 = 1400 + 120p + -1p2 + -1400 + -120p + p2 Reorder the terms: 3600 + -120p + p2 = 1400 + -1400 + 120p + -120p + -1p2 + p2 Combine like terms: 1400 + -1400 = 0 3600 + -120p + p2 = 0 + 120p + -120p + -1p2 + p2 3600 + -120p + p2 = 120p + -120p + -1p2 + p2 Combine like terms: 120p + -120p = 0 3600 + -120p + p2 = 0 + -1p2 + p2 3600 + -120p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 3600 + -120p + p2 = 0 Factor a trinomial. (60 + -1p)(60 + -1p) = 0Subproblem 1
Set the factor '(60 + -1p)' equal to zero and attempt to solve: Simplifying 60 + -1p = 0 Solving 60 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1p = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1p = 0 + -60 -1p = 0 + -60 Combine like terms: 0 + -60 = -60 -1p = -60 Divide each side by '-1'. p = 60 Simplifying p = 60Subproblem 2
Set the factor '(60 + -1p)' equal to zero and attempt to solve: Simplifying 60 + -1p = 0 Solving 60 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1p = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1p = 0 + -60 -1p = 0 + -60 Combine like terms: 0 + -60 = -60 -1p = -60 Divide each side by '-1'. p = 60 Simplifying p = 60Solution
p = {60, 60}
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