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Simplifying 0 = p2 + 15p + 56 Reorder the terms: 0 = 56 + 15p + p2 Solving 0 = 56 + 15p + p2 Solving for variable 'p'. Combine like terms: 0 + -56 = -56 -56 + -15p + -1p2 = 56 + 15p + p2 + -56 + -15p + -1p2 Reorder the terms: -56 + -15p + -1p2 = 56 + -56 + 15p + -15p + p2 + -1p2 Combine like terms: 56 + -56 = 0 -56 + -15p + -1p2 = 0 + 15p + -15p + p2 + -1p2 -56 + -15p + -1p2 = 15p + -15p + p2 + -1p2 Combine like terms: 15p + -15p = 0 -56 + -15p + -1p2 = 0 + p2 + -1p2 -56 + -15p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -56 + -15p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(56 + 15p + p2) = 0 Factor a trinomial. -1((8 + p)(7 + p)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + p)' equal to zero and attempt to solve: Simplifying 8 + p = 0 Solving 8 + p = 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 + p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + p = 0 + -8 p = 0 + -8 Combine like terms: 0 + -8 = -8 p = -8 Simplifying p = -8Subproblem 2
Set the factor '(7 + p)' equal to zero and attempt to solve: Simplifying 7 + p = 0 Solving 7 + p = 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 + p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + p = 0 + -7 p = 0 + -7 Combine like terms: 0 + -7 = -7 p = -7 Simplifying p = -7Solution
p = {-8, -7}
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