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Simplifying 4p2 + 42p = -80 Reorder the terms: 42p + 4p2 = -80 Solving 42p + 4p2 = -80 Solving for variable 'p'. Reorder the terms: 80 + 42p + 4p2 = -80 + 80 Combine like terms: -80 + 80 = 0 80 + 42p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(40 + 21p + 2p2) = 0 Factor a trinomial. 2((8 + p)(5 + 2p)) = 0 Ignore the factor 2.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 '(5 + 2p)' equal to zero and attempt to solve: Simplifying 5 + 2p = 0 Solving 5 + 2p = 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 + 2p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2p = 0 + -5 2p = 0 + -5 Combine like terms: 0 + -5 = -5 2p = -5 Divide each side by '2'. p = -2.5 Simplifying p = -2.5Solution
p = {-8, -2.5}
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