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Simplifying 12p2 + 14pq + -40q2 = 0 Reorder the terms: 14pq + 12p2 + -40q2 = 0 Solving 14pq + 12p2 + -40q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(7pq + 6p2 + -20q2) = 0 Factor a trinomial. 2((3p + -4q)(2p + 5q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3p + -4q)' equal to zero and attempt to solve: Simplifying 3p + -4q = 0 Solving 3p + -4q = 0 Move all terms containing p to the left, all other terms to the right. Add '4q' to each side of the equation. 3p + -4q + 4q = 0 + 4q Combine like terms: -4q + 4q = 0 3p + 0 = 0 + 4q 3p = 0 + 4q Remove the zero: 3p = 4q Divide each side by '3'. p = 1.333333333q Simplifying p = 1.333333333qSubproblem 2
Set the factor '(2p + 5q)' equal to zero and attempt to solve: Simplifying 2p + 5q = 0 Solving 2p + 5q = 0 Move all terms containing p to the left, all other terms to the right. Add '-5q' to each side of the equation. 2p + 5q + -5q = 0 + -5q Combine like terms: 5q + -5q = 0 2p + 0 = 0 + -5q 2p = 0 + -5q Remove the zero: 2p = -5q Divide each side by '2'. p = -2.5q Simplifying p = -2.5qSolution
p = {1.333333333q, -2.5q}
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