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Simplifying 7p2 + -91p = -280 Reorder the terms: -91p + 7p2 = -280 Solving -91p + 7p2 = -280 Solving for variable 'p'. Reorder the terms: 280 + -91p + 7p2 = -280 + 280 Combine like terms: -280 + 280 = 0 280 + -91p + 7p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(40 + -13p + p2) = 0 Factor a trinomial. 7((5 + -1p)(8 + -1p)) = 0 Ignore the factor 7.Subproblem 1
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 = 5Subproblem 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 = {5, 8}
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