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Simplifying 5p2 = -20 + 29p Solving 5p2 = -20 + 29p Solving for variable 'p'. Reorder the terms: 20 + -29p + 5p2 = -20 + 29p + 20 + -29p Reorder the terms: 20 + -29p + 5p2 = -20 + 20 + 29p + -29p Combine like terms: -20 + 20 = 0 20 + -29p + 5p2 = 0 + 29p + -29p 20 + -29p + 5p2 = 29p + -29p Combine like terms: 29p + -29p = 0 20 + -29p + 5p2 = 0 Factor a trinomial. (4 + -5p)(5 + -1p) = 0Subproblem 1
Set the factor '(4 + -5p)' equal to zero and attempt to solve: Simplifying 4 + -5p = 0 Solving 4 + -5p = 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 + -5p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5p = 0 + -4 -5p = 0 + -4 Combine like terms: 0 + -4 = -4 -5p = -4 Divide each side by '-5'. p = 0.8 Simplifying p = 0.8Subproblem 2
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 = 5Solution
p = {0.8, 5}
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