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Simplifying 4p2 = -24 + 35p Solving 4p2 = -24 + 35p Solving for variable 'p'. Reorder the terms: 24 + -35p + 4p2 = -24 + 35p + 24 + -35p Reorder the terms: 24 + -35p + 4p2 = -24 + 24 + 35p + -35p Combine like terms: -24 + 24 = 0 24 + -35p + 4p2 = 0 + 35p + -35p 24 + -35p + 4p2 = 35p + -35p Combine like terms: 35p + -35p = 0 24 + -35p + 4p2 = 0 Factor a trinomial. (3 + -4p)(8 + -1p) = 0Subproblem 1
Set the factor '(3 + -4p)' equal to zero and attempt to solve: Simplifying 3 + -4p = 0 Solving 3 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4p = 0 + -3 -4p = 0 + -3 Combine like terms: 0 + -3 = -3 -4p = -3 Divide each side by '-4'. p = 0.75 Simplifying p = 0.75Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve: Simplifying 8 + -1p = 0 Solving 8 + -1p = 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 + -1p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = 0 + -8 -1p = 0 + -8 Combine like terms: 0 + -8 = -8 -1p = -8 Divide each side by '-1'. p = 8 Simplifying p = 8Solution
p = {0.75, 8}
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