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Simplifying p2 = 85 + 12p Solving p2 = 85 + 12p Solving for variable 'p'. Reorder the terms: -85 + -12p + p2 = 85 + 12p + -85 + -12p Reorder the terms: -85 + -12p + p2 = 85 + -85 + 12p + -12p Combine like terms: 85 + -85 = 0 -85 + -12p + p2 = 0 + 12p + -12p -85 + -12p + p2 = 12p + -12p Combine like terms: 12p + -12p = 0 -85 + -12p + p2 = 0 Factor a trinomial. (-5 + -1p)(17 + -1p) = 0Subproblem 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 '(17 + -1p)' equal to zero and attempt to solve: Simplifying 17 + -1p = 0 Solving 17 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1p = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1p = 0 + -17 -1p = 0 + -17 Combine like terms: 0 + -17 = -17 -1p = -17 Divide each side by '-1'. p = 17 Simplifying p = 17Solution
p = {-5, 17}
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