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Simplifying 12p2 + 61pq + 5q2 = 0 Reorder the terms: 61pq + 12p2 + 5q2 = 0 Solving 61pq + 12p2 + 5q2 = 0 Solving for variable 'p'. Factor a trinomial. (12p + q)(p + 5q) = 0Subproblem 1
Set the factor '(12p + q)' equal to zero and attempt to solve: Simplifying 12p + q = 0 Solving 12p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 12p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 12p + 0 = 0 + -1q 12p = 0 + -1q Remove the zero: 12p = -1q Divide each side by '12'. p = -0.08333333333q Simplifying p = -0.08333333333qSubproblem 2
Set the factor '(p + 5q)' equal to zero and attempt to solve: Simplifying p + 5q = 0 Solving p + 5q = 0 Move all terms containing p to the left, all other terms to the right. Add '-5q' to each side of the equation. p + 5q + -5q = 0 + -5q Combine like terms: 5q + -5q = 0 p + 0 = 0 + -5q p = 0 + -5q Remove the zero: p = -5q Simplifying p = -5qSolution
p = {-0.08333333333q, -5q}
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