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Simplifying 0 = 24 + 10p + -1p2 Solving 0 = 24 + 10p + -1p2 Solving for variable 'p'. Combine like terms: 0 + -24 = -24 -24 + -10p + p2 = 24 + 10p + -1p2 + -24 + -10p + p2 Reorder the terms: -24 + -10p + p2 = 24 + -24 + 10p + -10p + -1p2 + p2 Combine like terms: 24 + -24 = 0 -24 + -10p + p2 = 0 + 10p + -10p + -1p2 + p2 -24 + -10p + p2 = 10p + -10p + -1p2 + p2 Combine like terms: 10p + -10p = 0 -24 + -10p + p2 = 0 + -1p2 + p2 -24 + -10p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -24 + -10p + p2 = 0 Factor a trinomial. (-2 + -1p)(12 + -1p) = 0Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve: Simplifying -2 + -1p = 0 Solving -2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1p = 0 + 2 -1p = 0 + 2 Combine like terms: 0 + 2 = 2 -1p = 2 Divide each side by '-1'. p = -2 Simplifying p = -2Subproblem 2
Set the factor '(12 + -1p)' equal to zero and attempt to solve: Simplifying 12 + -1p = 0 Solving 12 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1p = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1p = 0 + -12 -1p = 0 + -12 Combine like terms: 0 + -12 = -12 -1p = -12 Divide each side by '-1'. p = 12 Simplifying p = 12Solution
p = {-2, 12}
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