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Simplifying 2p2 = 3p + 20 Reorder the terms: 2p2 = 20 + 3p Solving 2p2 = 20 + 3p Solving for variable 'p'. Reorder the terms: -20 + -3p + 2p2 = 20 + 3p + -20 + -3p Reorder the terms: -20 + -3p + 2p2 = 20 + -20 + 3p + -3p Combine like terms: 20 + -20 = 0 -20 + -3p + 2p2 = 0 + 3p + -3p -20 + -3p + 2p2 = 3p + -3p Combine like terms: 3p + -3p = 0 -20 + -3p + 2p2 = 0 Factor a trinomial. (-5 + -2p)(4 + -1p) = 0Subproblem 1
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 = -2.5Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 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 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {-2.5, 4}
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