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Simplifying 8p2 + 11p + 20 = 6 + 6p2 Reorder the terms: 20 + 11p + 8p2 = 6 + 6p2 Solving 20 + 11p + 8p2 = 6 + 6p2 Solving for variable 'p'. Reorder the terms: 20 + -6 + 11p + 8p2 + -6p2 = 6 + 6p2 + -6 + -6p2 Combine like terms: 20 + -6 = 14 14 + 11p + 8p2 + -6p2 = 6 + 6p2 + -6 + -6p2 Combine like terms: 8p2 + -6p2 = 2p2 14 + 11p + 2p2 = 6 + 6p2 + -6 + -6p2 Reorder the terms: 14 + 11p + 2p2 = 6 + -6 + 6p2 + -6p2 Combine like terms: 6 + -6 = 0 14 + 11p + 2p2 = 0 + 6p2 + -6p2 14 + 11p + 2p2 = 6p2 + -6p2 Combine like terms: 6p2 + -6p2 = 0 14 + 11p + 2p2 = 0 Factor a trinomial. (7 + 2p)(2 + p) = 0Subproblem 1
Set the factor '(7 + 2p)' equal to zero and attempt to solve: Simplifying 7 + 2p = 0 Solving 7 + 2p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2p = 0 + -7 2p = 0 + -7 Combine like terms: 0 + -7 = -7 2p = -7 Divide each side by '2'. p = -3.5 Simplifying p = -3.5Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2Solution
p = {-3.5, -2}
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