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Simplifying p2 + -20p + -105 = -9 Reorder the terms: -105 + -20p + p2 = -9 Solving -105 + -20p + p2 = -9 Solving for variable 'p'. Reorder the terms: -105 + 9 + -20p + p2 = -9 + 9 Combine like terms: -105 + 9 = -96 -96 + -20p + p2 = -9 + 9 Combine like terms: -9 + 9 = 0 -96 + -20p + p2 = 0 Factor a trinomial. (-4 + -1p)(24 + -1p) = 0Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve: Simplifying -4 + -1p = 0 Solving -4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1p = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1p = 0 + 4 -1p = 0 + 4 Combine like terms: 0 + 4 = 4 -1p = 4 Divide each side by '-1'. p = -4 Simplifying p = -4Subproblem 2
Set the factor '(24 + -1p)' equal to zero and attempt to solve: Simplifying 24 + -1p = 0 Solving 24 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1p = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1p = 0 + -24 -1p = 0 + -24 Combine like terms: 0 + -24 = -24 -1p = -24 Divide each side by '-1'. p = 24 Simplifying p = 24Solution
p = {-4, 24}
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