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Simplifying 23P = 5P2 + 24 Reorder the terms: 23P = 24 + 5P2 Solving 23P = 24 + 5P2 Solving for variable 'P'. Reorder the terms: -24 + 23P + -5P2 = 24 + 5P2 + -24 + -5P2 Reorder the terms: -24 + 23P + -5P2 = 24 + -24 + 5P2 + -5P2 Combine like terms: 24 + -24 = 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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