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Simplifying 2400 = (1100 + -100p) * p Reorder the terms for easier multiplication: 2400 = p(1100 + -100p) 2400 = (1100 * p + -100p * p) 2400 = (1100p + -100p2) Solving 2400 = 1100p + -100p2 Solving for variable 'p'. Reorder the terms: 2400 + -1100p + 100p2 = 1100p + -1100p + -100p2 + 100p2 Combine like terms: 1100p + -1100p = 0 2400 + -1100p + 100p2 = 0 + -100p2 + 100p2 2400 + -1100p + 100p2 = -100p2 + 100p2 Combine like terms: -100p2 + 100p2 = 0 2400 + -1100p + 100p2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(24 + -11p + p2) = 0 Factor a trinomial. 100((3 + -1p)(8 + -1p)) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Solution
p = {3, 8}
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