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Simplifying 0 = 5p2 + -23p + 24 Reorder the terms: 0 = 24 + -23p + 5p2 Solving 0 = 24 + -23p + 5p2 Solving for variable 'p'. Combine like terms: 0 + -24 = -24 -24 + 23p + -5p2 = 24 + -23p + 5p2 + -24 + 23p + -5p2 Reorder the terms: -24 + 23p + -5p2 = 24 + -24 + -23p + 23p + 5p2 + -5p2 Combine like terms: 24 + -24 = 0 -24 + 23p + -5p2 = 0 + -23p + 23p + 5p2 + -5p2 -24 + 23p + -5p2 = -23p + 23p + 5p2 + -5p2 Combine like terms: -23p + 23p = 0 -24 + 23p + -5p2 = 0 + 5p2 + -5p2 -24 + 23p + -5p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 -24 + 23p + -5p2 = 0 Factor a trinomial. (-3 + p)(8 + -5p) = 0Subproblem 1
Set the factor '(-3 + p)' equal to zero and attempt to solve: Simplifying -3 + p = 0 Solving -3 + p = 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 + p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + p = 0 + 3 p = 0 + 3 Combine like terms: 0 + 3 = 3 p = 3 Simplifying p = 3Subproblem 2
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 = 1.6Solution
p = {3, 1.6}
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