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Simplifying p2 = 12p + -27 Reorder the terms: p2 = -27 + 12p Solving p2 = -27 + 12p Solving for variable 'p'. Reorder the terms: 27 + -12p + p2 = -27 + 12p + 27 + -12p Reorder the terms: 27 + -12p + p2 = -27 + 27 + 12p + -12p Combine like terms: -27 + 27 = 0 27 + -12p + p2 = 0 + 12p + -12p 27 + -12p + p2 = 12p + -12p Combine like terms: 12p + -12p = 0 27 + -12p + p2 = 0 Factor a trinomial. (3 + -1p)(9 + -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 '(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 = 9Solution
p = {3, 9}
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