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Simplifying -5 = 2p + -16p2 Solving -5 = 2p + -16p2 Solving for variable 'p'. Reorder the terms: -5 + -2p + 16p2 = 2p + -2p + -16p2 + 16p2 Combine like terms: 2p + -2p = 0 -5 + -2p + 16p2 = 0 + -16p2 + 16p2 -5 + -2p + 16p2 = -16p2 + 16p2 Combine like terms: -16p2 + 16p2 = 0 -5 + -2p + 16p2 = 0 Factor a trinomial. (-1 + -2p)(5 + -8p) = 0Subproblem 1
Set the factor '(-1 + -2p)' equal to zero and attempt to solve: Simplifying -1 + -2p = 0 Solving -1 + -2p = 0 Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2p = 0 + 1 -2p = 0 + 1 Combine like terms: 0 + 1 = 1 -2p = 1 Divide each side by '-2'. p = -0.5 Simplifying p = -0.5Subproblem 2
Set the factor '(5 + -8p)' equal to zero and attempt to solve: Simplifying 5 + -8p = 0 Solving 5 + -8p = 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 + -8p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8p = 0 + -5 -8p = 0 + -5 Combine like terms: 0 + -5 = -5 -8p = -5 Divide each side by '-8'. p = 0.625 Simplifying p = 0.625Solution
p = {-0.5, 0.625}
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