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Simplifying -8p2 + -4p = -23p2 + 4p + -1 Reorder the terms: -4p + -8p2 = -23p2 + 4p + -1 Reorder the terms: -4p + -8p2 = -1 + 4p + -23p2 Solving -4p + -8p2 = -1 + 4p + -23p2 Solving for variable 'p'. Reorder the terms: 1 + -4p + -4p + -8p2 + 23p2 = -1 + 4p + -23p2 + 1 + -4p + 23p2 Combine like terms: -4p + -4p = -8p 1 + -8p + -8p2 + 23p2 = -1 + 4p + -23p2 + 1 + -4p + 23p2 Combine like terms: -8p2 + 23p2 = 15p2 1 + -8p + 15p2 = -1 + 4p + -23p2 + 1 + -4p + 23p2 Reorder the terms: 1 + -8p + 15p2 = -1 + 1 + 4p + -4p + -23p2 + 23p2 Combine like terms: -1 + 1 = 0 1 + -8p + 15p2 = 0 + 4p + -4p + -23p2 + 23p2 1 + -8p + 15p2 = 4p + -4p + -23p2 + 23p2 Combine like terms: 4p + -4p = 0 1 + -8p + 15p2 = 0 + -23p2 + 23p2 1 + -8p + 15p2 = -23p2 + 23p2 Combine like terms: -23p2 + 23p2 = 0 1 + -8p + 15p2 = 0 Factor a trinomial. (1 + -5p)(1 + -3p) = 0Subproblem 1
Set the factor '(1 + -5p)' equal to zero and attempt to solve: Simplifying 1 + -5p = 0 Solving 1 + -5p = 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 + -5p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5p = 0 + -1 -5p = 0 + -1 Combine like terms: 0 + -1 = -1 -5p = -1 Divide each side by '-5'. p = 0.2 Simplifying p = 0.2Subproblem 2
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 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 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Solution
p = {0.2, 0.3333333333}
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