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Simplifying (9p + -8)(9p + -8) = -2(9p + -8) + 15 Reorder the terms: (-8 + 9p)(9p + -8) = -2(9p + -8) + 15 Reorder the terms: (-8 + 9p)(-8 + 9p) = -2(9p + -8) + 15 Multiply (-8 + 9p) * (-8 + 9p) (-8(-8 + 9p) + 9p * (-8 + 9p)) = -2(9p + -8) + 15 ((-8 * -8 + 9p * -8) + 9p * (-8 + 9p)) = -2(9p + -8) + 15 ((64 + -72p) + 9p * (-8 + 9p)) = -2(9p + -8) + 15 (64 + -72p + (-8 * 9p + 9p * 9p)) = -2(9p + -8) + 15 (64 + -72p + (-72p + 81p2)) = -2(9p + -8) + 15 Combine like terms: -72p + -72p = -144p (64 + -144p + 81p2) = -2(9p + -8) + 15 Reorder the terms: 64 + -144p + 81p2 = -2(-8 + 9p) + 15 64 + -144p + 81p2 = (-8 * -2 + 9p * -2) + 15 64 + -144p + 81p2 = (16 + -18p) + 15 Reorder the terms: 64 + -144p + 81p2 = 16 + 15 + -18p Combine like terms: 16 + 15 = 31 64 + -144p + 81p2 = 31 + -18p Solving 64 + -144p + 81p2 = 31 + -18p Solving for variable 'p'. Reorder the terms: 64 + -31 + -144p + 18p + 81p2 = 31 + -18p + -31 + 18p Combine like terms: 64 + -31 = 33 33 + -144p + 18p + 81p2 = 31 + -18p + -31 + 18p Combine like terms: -144p + 18p = -126p 33 + -126p + 81p2 = 31 + -18p + -31 + 18p Reorder the terms: 33 + -126p + 81p2 = 31 + -31 + -18p + 18p Combine like terms: 31 + -31 = 0 33 + -126p + 81p2 = 0 + -18p + 18p 33 + -126p + 81p2 = -18p + 18p Combine like terms: -18p + 18p = 0 33 + -126p + 81p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + -42p + 27p2) = 0 Factor a trinomial. 3((1 + -3p)(11 + -9p)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 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 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Subproblem 2
Set the factor '(11 + -9p)' equal to zero and attempt to solve: Simplifying 11 + -9p = 0 Solving 11 + -9p = 0 Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -9p = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -9p = 0 + -11 -9p = 0 + -11 Combine like terms: 0 + -11 = -11 -9p = -11 Divide each side by '-9'. p = 1.222222222 Simplifying p = 1.222222222Solution
p = {0.3333333333, 1.222222222}
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