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Simplifying 0 = p2 + 6p + 5 Reorder the terms: 0 = 5 + 6p + p2 Solving 0 = 5 + 6p + p2 Solving for variable 'p'. Combine like terms: 0 + -5 = -5 -5 + -6p + -1p2 = 5 + 6p + p2 + -5 + -6p + -1p2 Reorder the terms: -5 + -6p + -1p2 = 5 + -5 + 6p + -6p + p2 + -1p2 Combine like terms: 5 + -5 = 0 -5 + -6p + -1p2 = 0 + 6p + -6p + p2 + -1p2 -5 + -6p + -1p2 = 6p + -6p + p2 + -1p2 Combine like terms: 6p + -6p = 0 -5 + -6p + -1p2 = 0 + p2 + -1p2 -5 + -6p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -5 + -6p + -1p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 6p + p2) = 0 Factor a trinomial. -1((5 + p)(1 + p)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve: Simplifying 5 + p = 0 Solving 5 + p = 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 + p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + p = 0 + -5 p = 0 + -5 Combine like terms: 0 + -5 = -5 p = -5 Simplifying p = -5Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve: Simplifying 1 + p = 0 Solving 1 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + p = 0 + -1 p = 0 + -1 Combine like terms: 0 + -1 = -1 p = -1 Simplifying p = -1Solution
p = {-5, -1}
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