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Simplifying -2p2 + 2p + 40 = 0 Reorder the terms: 40 + 2p + -2p2 = 0 Solving 40 + 2p + -2p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + p + -1p2) = 0 Factor a trinomial. 2((5 + -1p)(4 + p)) = 0 Ignore the factor 2.Subproblem 1
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 = 5Subproblem 2
Set the factor '(4 + p)' equal to zero and attempt to solve: Simplifying 4 + p = 0 Solving 4 + p = 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 + p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + p = 0 + -4 p = 0 + -4 Combine like terms: 0 + -4 = -4 p = -4 Simplifying p = -4Solution
p = {5, -4}
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