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Simplifying p2 = 5p + 24 Reorder the terms: p2 = 24 + 5p Solving p2 = 24 + 5p Solving for variable 'p'. Reorder the terms: -24 + -5p + p2 = 24 + 5p + -24 + -5p Reorder the terms: -24 + -5p + p2 = 24 + -24 + 5p + -5p Combine like terms: 24 + -24 = 0 -24 + -5p + p2 = 0 + 5p + -5p -24 + -5p + p2 = 5p + -5p Combine like terms: 5p + -5p = 0 -24 + -5p + p2 = 0 Factor a trinomial. (-3 + -1p)(8 + -1p) = 0Subproblem 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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