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Simplifying -2p2 + 46p = -48 Reorder the terms: 46p + -2p2 = -48 Solving 46p + -2p2 = -48 Solving for variable 'p'. Reorder the terms: 48 + 46p + -2p2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + 46p + -2p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 23p + -1p2) = 0 Factor a trinomial. 2((24 + -1p)(1 + p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + -1p)' equal to zero and attempt to solve: Simplifying 24 + -1p = 0 Solving 24 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1p = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1p = 0 + -24 -1p = 0 + -24 Combine like terms: 0 + -24 = -24 -1p = -24 Divide each side by '-1'. p = 24 Simplifying p = 24Subproblem 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 = {24, -1}
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