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Simplifying 117p2 + 2pq + -24q2 = 0 Reorder the terms: 2pq + 117p2 + -24q2 = 0 Solving 2pq + 117p2 + -24q2 = 0 Solving for variable 'p'. Factor a trinomial. (9p + -4q)(13p + 6q) = 0Subproblem 1
Set the factor '(9p + -4q)' equal to zero and attempt to solve: Simplifying 9p + -4q = 0 Solving 9p + -4q = 0 Move all terms containing p to the left, all other terms to the right. Add '4q' to each side of the equation. 9p + -4q + 4q = 0 + 4q Combine like terms: -4q + 4q = 0 9p + 0 = 0 + 4q 9p = 0 + 4q Remove the zero: 9p = 4q Divide each side by '9'. p = 0.4444444444q Simplifying p = 0.4444444444qSubproblem 2
Set the factor '(13p + 6q)' equal to zero and attempt to solve: Simplifying 13p + 6q = 0 Solving 13p + 6q = 0 Move all terms containing p to the left, all other terms to the right. Add '-6q' to each side of the equation. 13p + 6q + -6q = 0 + -6q Combine like terms: 6q + -6q = 0 13p + 0 = 0 + -6q 13p = 0 + -6q Remove the zero: 13p = -6q Divide each side by '13'. p = -0.4615384615q Simplifying p = -0.4615384615qSolution
p = {0.4444444444q, -0.4615384615q}
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