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Simplifying (p + 8)(p + -5) = 14 Reorder the terms: (8 + p)(p + -5) = 14 Reorder the terms: (8 + p)(-5 + p) = 14 Multiply (8 + p) * (-5 + p) (8(-5 + p) + p(-5 + p)) = 14 ((-5 * 8 + p * 8) + p(-5 + p)) = 14 ((-40 + 8p) + p(-5 + p)) = 14 (-40 + 8p + (-5 * p + p * p)) = 14 (-40 + 8p + (-5p + p2)) = 14 Combine like terms: 8p + -5p = 3p (-40 + 3p + p2) = 14 Solving -40 + 3p + p2 = 14 Solving for variable 'p'. Reorder the terms: -40 + -14 + 3p + p2 = 14 + -14 Combine like terms: -40 + -14 = -54 -54 + 3p + p2 = 14 + -14 Combine like terms: 14 + -14 = 0 -54 + 3p + p2 = 0 Factor a trinomial. (-9 + -1p)(6 + -1p) = 0Subproblem 1
Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve: Simplifying 6 + -1p = 0 Solving 6 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1p = 0 + -6 -1p = 0 + -6 Combine like terms: 0 + -6 = -6 -1p = -6 Divide each side by '-1'. p = 6 Simplifying p = 6Solution
p = {-9, 6}
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