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Simplifying 27p2 + 231p + -108 = 0 Reorder the terms: -108 + 231p + 27p2 = 0 Solving -108 + 231p + 27p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + 77p + 9p2) = 0 Factor a trinomial. 3((-9 + -1p)(4 + -9p)) = 0 Ignore the factor 3.Subproblem 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 '(4 + -9p)' equal to zero and attempt to solve: Simplifying 4 + -9p = 0 Solving 4 + -9p = 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 + -9p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9p = 0 + -4 -9p = 0 + -4 Combine like terms: 0 + -4 = -4 -9p = -4 Divide each side by '-9'. p = 0.4444444444 Simplifying p = 0.4444444444Solution
p = {-9, 0.4444444444}
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