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Simplifying (8p + 7)(8p + 7) = 7(8p + 7) + -6 Reorder the terms: (7 + 8p)(8p + 7) = 7(8p + 7) + -6 Reorder the terms: (7 + 8p)(7 + 8p) = 7(8p + 7) + -6 Multiply (7 + 8p) * (7 + 8p) (7(7 + 8p) + 8p * (7 + 8p)) = 7(8p + 7) + -6 ((7 * 7 + 8p * 7) + 8p * (7 + 8p)) = 7(8p + 7) + -6 ((49 + 56p) + 8p * (7 + 8p)) = 7(8p + 7) + -6 (49 + 56p + (7 * 8p + 8p * 8p)) = 7(8p + 7) + -6 (49 + 56p + (56p + 64p2)) = 7(8p + 7) + -6 Combine like terms: 56p + 56p = 112p (49 + 112p + 64p2) = 7(8p + 7) + -6 Reorder the terms: 49 + 112p + 64p2 = 7(7 + 8p) + -6 49 + 112p + 64p2 = (7 * 7 + 8p * 7) + -6 49 + 112p + 64p2 = (49 + 56p) + -6 Reorder the terms: 49 + 112p + 64p2 = 49 + -6 + 56p Combine like terms: 49 + -6 = 43 49 + 112p + 64p2 = 43 + 56p Solving 49 + 112p + 64p2 = 43 + 56p Solving for variable 'p'. Reorder the terms: 49 + -43 + 112p + -56p + 64p2 = 43 + 56p + -43 + -56p Combine like terms: 49 + -43 = 6 6 + 112p + -56p + 64p2 = 43 + 56p + -43 + -56p Combine like terms: 112p + -56p = 56p 6 + 56p + 64p2 = 43 + 56p + -43 + -56p Reorder the terms: 6 + 56p + 64p2 = 43 + -43 + 56p + -56p Combine like terms: 43 + -43 = 0 6 + 56p + 64p2 = 0 + 56p + -56p 6 + 56p + 64p2 = 56p + -56p Combine like terms: 56p + -56p = 0 6 + 56p + 64p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 28p + 32p2) = 0 Factor a trinomial. 2((3 + 4p)(1 + 8p)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 4p)' equal to zero and attempt to solve: Simplifying 3 + 4p = 0 Solving 3 + 4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4p = 0 + -3 4p = 0 + -3 Combine like terms: 0 + -3 = -3 4p = -3 Divide each side by '4'. p = -0.75 Simplifying p = -0.75Subproblem 2
Set the factor '(1 + 8p)' equal to zero and attempt to solve: Simplifying 1 + 8p = 0 Solving 1 + 8p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8p = 0 + -1 8p = 0 + -1 Combine like terms: 0 + -1 = -1 8p = -1 Divide each side by '8'. p = -0.125 Simplifying p = -0.125Solution
p = {-0.75, -0.125}
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