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Simplifying 2p(p + 4) = p2 + 5p + 10 Reorder the terms: 2p(4 + p) = p2 + 5p + 10 (4 * 2p + p * 2p) = p2 + 5p + 10 (8p + 2p2) = p2 + 5p + 10 Reorder the terms: 8p + 2p2 = 10 + 5p + p2 Solving 8p + 2p2 = 10 + 5p + p2 Solving for variable 'p'. Reorder the terms: -10 + 8p + -5p + 2p2 + -1p2 = 10 + 5p + p2 + -10 + -5p + -1p2 Combine like terms: 8p + -5p = 3p -10 + 3p + 2p2 + -1p2 = 10 + 5p + p2 + -10 + -5p + -1p2 Combine like terms: 2p2 + -1p2 = 1p2 -10 + 3p + 1p2 = 10 + 5p + p2 + -10 + -5p + -1p2 Reorder the terms: -10 + 3p + 1p2 = 10 + -10 + 5p + -5p + p2 + -1p2 Combine like terms: 10 + -10 = 0 -10 + 3p + 1p2 = 0 + 5p + -5p + p2 + -1p2 -10 + 3p + 1p2 = 5p + -5p + p2 + -1p2 Combine like terms: 5p + -5p = 0 -10 + 3p + 1p2 = 0 + p2 + -1p2 -10 + 3p + 1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 -10 + 3p + 1p2 = 0 Factor a trinomial. (-5 + -1p)(2 + -1p) = 0Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve: Simplifying -5 + -1p = 0 Solving -5 + -1p = 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 + -1p = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1p = 0 + 5 -1p = 0 + 5 Combine like terms: 0 + 5 = 5 -1p = 5 Divide each side by '-1'. p = -5 Simplifying p = -5Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 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 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2Solution
p = {-5, 2}
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