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Simplifying p2 + 5p + -31 = -7 Reorder the terms: -31 + 5p + p2 = -7 Solving -31 + 5p + p2 = -7 Solving for variable 'p'. Reorder the terms: -31 + 7 + 5p + p2 = -7 + 7 Combine like terms: -31 + 7 = -24 -24 + 5p + p2 = -7 + 7 Combine like terms: -7 + 7 = 0 -24 + 5p + p2 = 0 Factor a trinomial. (-8 + -1p)(3 + -1p) = 0Subproblem 1
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 = -8Subproblem 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 = {-8, 3}
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