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Simplifying (11p + 6q)(-2p + 8q) = 0 Multiply (11p + 6q) * (-2p + 8q) (11p * (-2p + 8q) + 6q * (-2p + 8q)) = 0 ((-2p * 11p + 8q * 11p) + 6q * (-2p + 8q)) = 0 Reorder the terms: ((88pq + -22p2) + 6q * (-2p + 8q)) = 0 ((88pq + -22p2) + 6q * (-2p + 8q)) = 0 (88pq + -22p2 + (-2p * 6q + 8q * 6q)) = 0 (88pq + -22p2 + (-12pq + 48q2)) = 0 Reorder the terms: (88pq + -12pq + -22p2 + 48q2) = 0 Combine like terms: 88pq + -12pq = 76pq (76pq + -22p2 + 48q2) = 0 Solving 76pq + -22p2 + 48q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(38pq + -11p2 + 24q2) = 0 Factor a trinomial. 2((-11p + -6q)(p + -4q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11p + -6q)' equal to zero and attempt to solve: Simplifying -11p + -6q = 0 Solving -11p + -6q = 0 Move all terms containing p to the left, all other terms to the right. Add '6q' to each side of the equation. -11p + -6q + 6q = 0 + 6q Combine like terms: -6q + 6q = 0 -11p + 0 = 0 + 6q -11p = 0 + 6q Remove the zero: -11p = 6q Divide each side by '-11'. p = -0.5454545455q Simplifying p = -0.5454545455qSubproblem 2
Set the factor '(p + -4q)' equal to zero and attempt to solve: Simplifying p + -4q = 0 Solving p + -4q = 0 Move all terms containing p to the left, all other terms to the right. Add '4q' to each side of the equation. p + -4q + 4q = 0 + 4q Combine like terms: -4q + 4q = 0 p + 0 = 0 + 4q p = 0 + 4q Remove the zero: p = 4q Simplifying p = 4qSolution
p = {-0.5454545455q, 4q}
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