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Simplifying 5p2 + -18p + -27 = 8 Reorder the terms: -27 + -18p + 5p2 = 8 Solving -27 + -18p + 5p2 = 8 Solving for variable 'p'. Reorder the terms: -27 + -8 + -18p + 5p2 = 8 + -8 Combine like terms: -27 + -8 = -35 -35 + -18p + 5p2 = 8 + -8 Combine like terms: 8 + -8 = 0 -35 + -18p + 5p2 = 0 Factor a trinomial. (-7 + -5p)(5 + -1p) = 0Subproblem 1
Set the factor '(-7 + -5p)' equal to zero and attempt to solve: Simplifying -7 + -5p = 0 Solving -7 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5p = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5p = 0 + 7 -5p = 0 + 7 Combine like terms: 0 + 7 = 7 -5p = 7 Divide each side by '-5'. p = -1.4 Simplifying p = -1.4Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5Solution
p = {-1.4, 5}
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