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Simplifying p2 = 5p + 14 Reorder the terms: p2 = 14 + 5p Solving p2 = 14 + 5p Solving for variable 'p'. Reorder the terms: -14 + -5p + p2 = 14 + 5p + -14 + -5p Reorder the terms: -14 + -5p + p2 = 14 + -14 + 5p + -5p Combine like terms: 14 + -14 = 0 -14 + -5p + p2 = 0 + 5p + -5p -14 + -5p + p2 = 5p + -5p Combine like terms: 5p + -5p = 0 -14 + -5p + p2 = 0 Factor a trinomial. (-2 + -1p)(7 + -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 '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7Solution
p = {-2, 7}
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