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Simplifying 10p2 + 31pq + -14q2 = 0 Reorder the terms: 31pq + 10p2 + -14q2 = 0 Solving 31pq + 10p2 + -14q2 = 0 Solving for variable 'p'. Factor a trinomial. (5p + -2q)(2p + 7q) = 0Subproblem 1
Set the factor '(5p + -2q)' equal to zero and attempt to solve: Simplifying 5p + -2q = 0 Solving 5p + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. 5p + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 5p + 0 = 0 + 2q 5p = 0 + 2q Remove the zero: 5p = 2q Divide each side by '5'. p = 0.4q Simplifying p = 0.4qSubproblem 2
Set the factor '(2p + 7q)' equal to zero and attempt to solve: Simplifying 2p + 7q = 0 Solving 2p + 7q = 0 Move all terms containing p to the left, all other terms to the right. Add '-7q' to each side of the equation. 2p + 7q + -7q = 0 + -7q Combine like terms: 7q + -7q = 0 2p + 0 = 0 + -7q 2p = 0 + -7q Remove the zero: 2p = -7q Divide each side by '2'. p = -3.5q Simplifying p = -3.5qSolution
p = {0.4q, -3.5q}
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