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Simplifying 7p2 = 56 + 14p Solving 7p2 = 56 + 14p Solving for variable 'p'. Reorder the terms: -56 + -14p + 7p2 = 56 + 14p + -56 + -14p Reorder the terms: -56 + -14p + 7p2 = 56 + -56 + 14p + -14p Combine like terms: 56 + -56 = 0 -56 + -14p + 7p2 = 0 + 14p + -14p -56 + -14p + 7p2 = 14p + -14p Combine like terms: 14p + -14p = 0 -56 + -14p + 7p2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-8 + -2p + p2) = 0 Factor a trinomial. 7((-2 + -1p)(4 + -1p)) = 0 Ignore the factor 7.Subproblem 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 '(4 + -1p)' equal to zero and attempt to solve: Simplifying 4 + -1p = 0 Solving 4 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1p = 0 + -4 -1p = 0 + -4 Combine like terms: 0 + -4 = -4 -1p = -4 Divide each side by '-1'. p = 4 Simplifying p = 4Solution
p = {-2, 4}
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