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Simplifying p2 = 27 + -6p Solving p2 = 27 + -6p Solving for variable 'p'. Reorder the terms: -27 + 6p + p2 = 27 + -6p + -27 + 6p Reorder the terms: -27 + 6p + p2 = 27 + -27 + -6p + 6p Combine like terms: 27 + -27 = 0 -27 + 6p + p2 = 0 + -6p + 6p -27 + 6p + p2 = -6p + 6p Combine like terms: -6p + 6p = 0 -27 + 6p + p2 = 0 Factor a trinomial. (-9 + -1p)(3 + -1p) = 0Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9Subproblem 2
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 = 3Solution
p = {-9, 3}
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