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Simplifying 8p2 = 112 + 0 + 40p Combine like terms: 112 + 0 = 112 8p2 = 112 + 40p Solving 8p2 = 112 + 40p Solving for variable 'p'. Reorder the terms: -112 + -40p + 8p2 = 112 + 40p + -112 + -40p Reorder the terms: -112 + -40p + 8p2 = 112 + -112 + 40p + -40p Combine like terms: 112 + -112 = 0 -112 + -40p + 8p2 = 0 + 40p + -40p -112 + -40p + 8p2 = 40p + -40p Combine like terms: 40p + -40p = 0 -112 + -40p + 8p2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-14 + -5p + p2) = 0 Factor a trinomial. 8((-2 + -1p)(7 + -1p)) = 0 Ignore the factor 8.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 '(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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