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Simplifying (p + -11)(p + -5) + (2p + 9)(p + 9) = 2p2 + 6p + 172 Reorder the terms: (-11 + p)(p + -5) + (2p + 9)(p + 9) = 2p2 + 6p + 172 Reorder the terms: (-11 + p)(-5 + p) + (2p + 9)(p + 9) = 2p2 + 6p + 172 Multiply (-11 + p) * (-5 + p) (-11(-5 + p) + p(-5 + p)) + (2p + 9)(p + 9) = 2p2 + 6p + 172 ((-5 * -11 + p * -11) + p(-5 + p)) + (2p + 9)(p + 9) = 2p2 + 6p + 172 ((55 + -11p) + p(-5 + p)) + (2p + 9)(p + 9) = 2p2 + 6p + 172 (55 + -11p + (-5 * p + p * p)) + (2p + 9)(p + 9) = 2p2 + 6p + 172 (55 + -11p + (-5p + p2)) + (2p + 9)(p + 9) = 2p2 + 6p + 172 Combine like terms: -11p + -5p = -16p (55 + -16p + p2) + (2p + 9)(p + 9) = 2p2 + 6p + 172 Reorder the terms: 55 + -16p + p2 + (9 + 2p)(p + 9) = 2p2 + 6p + 172 Reorder the terms: 55 + -16p + p2 + (9 + 2p)(9 + p) = 2p2 + 6p + 172 Multiply (9 + 2p) * (9 + p) 55 + -16p + p2 + (9(9 + p) + 2p * (9 + p)) = 2p2 + 6p + 172 55 + -16p + p2 + ((9 * 9 + p * 9) + 2p * (9 + p)) = 2p2 + 6p + 172 55 + -16p + p2 + ((81 + 9p) + 2p * (9 + p)) = 2p2 + 6p + 172 55 + -16p + p2 + (81 + 9p + (9 * 2p + p * 2p)) = 2p2 + 6p + 172 55 + -16p + p2 + (81 + 9p + (18p + 2p2)) = 2p2 + 6p + 172 Combine like terms: 9p + 18p = 27p 55 + -16p + p2 + (81 + 27p + 2p2) = 2p2 + 6p + 172 Reorder the terms: 55 + 81 + -16p + 27p + p2 + 2p2 = 2p2 + 6p + 172 Combine like terms: 55 + 81 = 136 136 + -16p + 27p + p2 + 2p2 = 2p2 + 6p + 172 Combine like terms: -16p + 27p = 11p 136 + 11p + p2 + 2p2 = 2p2 + 6p + 172 Combine like terms: p2 + 2p2 = 3p2 136 + 11p + 3p2 = 2p2 + 6p + 172 Reorder the terms: 136 + 11p + 3p2 = 172 + 6p + 2p2 Solving 136 + 11p + 3p2 = 172 + 6p + 2p2 Solving for variable 'p'. Reorder the terms: 136 + -172 + 11p + -6p + 3p2 + -2p2 = 172 + 6p + 2p2 + -172 + -6p + -2p2 Combine like terms: 136 + -172 = -36 -36 + 11p + -6p + 3p2 + -2p2 = 172 + 6p + 2p2 + -172 + -6p + -2p2 Combine like terms: 11p + -6p = 5p -36 + 5p + 3p2 + -2p2 = 172 + 6p + 2p2 + -172 + -6p + -2p2 Combine like terms: 3p2 + -2p2 = 1p2 -36 + 5p + 1p2 = 172 + 6p + 2p2 + -172 + -6p + -2p2 Reorder the terms: -36 + 5p + 1p2 = 172 + -172 + 6p + -6p + 2p2 + -2p2 Combine like terms: 172 + -172 = 0 -36 + 5p + 1p2 = 0 + 6p + -6p + 2p2 + -2p2 -36 + 5p + 1p2 = 6p + -6p + 2p2 + -2p2 Combine like terms: 6p + -6p = 0 -36 + 5p + 1p2 = 0 + 2p2 + -2p2 -36 + 5p + 1p2 = 2p2 + -2p2 Combine like terms: 2p2 + -2p2 = 0 -36 + 5p + 1p2 = 0 Factor a trinomial. (-9 + -1p)(4 + -1p) = 0Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9Subproblem 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 = {-9, 4}
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