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Simplifying (10p2 + 11p + -8) = 0 Reorder the terms: (-8 + 11p + 10p2) = 0 Remove parenthesis around (-8 + 11p + 10p2) -8 + 11p + 10p2 = 0 Solving -8 + 11p + 10p2 = 0 Solving for variable 'p'. Factor a trinomial. (-8 + -5p)(1 + -2p) = 0Subproblem 1
Set the factor '(-8 + -5p)' equal to zero and attempt to solve: Simplifying -8 + -5p = 0 Solving -8 + -5p = 0 Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5p = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5p = 0 + 8 -5p = 0 + 8 Combine like terms: 0 + 8 = 8 -5p = 8 Divide each side by '-5'. p = -1.6 Simplifying p = -1.6Subproblem 2
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 = 0.5Solution
p = {-1.6, 0.5}
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