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Simplifying 400 = 60p + 4p2 Solving 400 = 60p + 4p2 Solving for variable 'p'. Reorder the terms: 400 + -60p + -4p2 = 60p + -60p + 4p2 + -4p2 Combine like terms: 60p + -60p = 0 400 + -60p + -4p2 = 0 + 4p2 + -4p2 400 + -60p + -4p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 400 + -60p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + -15p + -1p2) = 0 Factor a trinomial. 4((5 + -1p)(20 + p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Subproblem 2
Set the factor '(20 + p)' equal to zero and attempt to solve: Simplifying 20 + p = 0 Solving 20 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + p = 0 + -20 Combine like terms: 20 + -20 = 0 0 + p = 0 + -20 p = 0 + -20 Combine like terms: 0 + -20 = -20 p = -20 Simplifying p = -20Solution
p = {5, -20}
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