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Simplifying 0 = -2p2 + 200p + -5000 Reorder the terms: 0 = -5000 + 200p + -2p2 Solving 0 = -5000 + 200p + -2p2 Solving for variable 'p'. Combine like terms: 0 + 5000 = 5000 5000 + -200p + 2p2 = -5000 + 200p + -2p2 + 5000 + -200p + 2p2 Reorder the terms: 5000 + -200p + 2p2 = -5000 + 5000 + 200p + -200p + -2p2 + 2p2 Combine like terms: -5000 + 5000 = 0 5000 + -200p + 2p2 = 0 + 200p + -200p + -2p2 + 2p2 5000 + -200p + 2p2 = 200p + -200p + -2p2 + 2p2 Combine like terms: 200p + -200p = 0 5000 + -200p + 2p2 = 0 + -2p2 + 2p2 5000 + -200p + 2p2 = -2p2 + 2p2 Combine like terms: -2p2 + 2p2 = 0 5000 + -200p + 2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2500 + -100p + p2) = 0 Factor a trinomial. 2((50 + -1p)(50 + -1p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -1p)' equal to zero and attempt to solve: Simplifying 50 + -1p = 0 Solving 50 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1p = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1p = 0 + -50 -1p = 0 + -50 Combine like terms: 0 + -50 = -50 -1p = -50 Divide each side by '-1'. p = 50 Simplifying p = 50Subproblem 2
Set the factor '(50 + -1p)' equal to zero and attempt to solve: Simplifying 50 + -1p = 0 Solving 50 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1p = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1p = 0 + -50 -1p = 0 + -50 Combine like terms: 0 + -50 = -50 -1p = -50 Divide each side by '-1'. p = 50 Simplifying p = 50Solution
p = {50, 50}
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