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Simplifying 3p2 + -10pq + 3q2 = 0 Reorder the terms: -10pq + 3p2 + 3q2 = 0 Solving -10pq + 3p2 + 3q2 = 0 Solving for variable 'p'. Factor a trinomial. (p + -3q)(3p + -1q) = 0Subproblem 1
Set the factor '(p + -3q)' equal to zero and attempt to solve: Simplifying p + -3q = 0 Solving p + -3q = 0 Move all terms containing p to the left, all other terms to the right. Add '3q' to each side of the equation. p + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 p + 0 = 0 + 3q p = 0 + 3q Remove the zero: p = 3q Simplifying p = 3qSubproblem 2
Set the factor '(3p + -1q)' equal to zero and attempt to solve: Simplifying 3p + -1q = 0 Solving 3p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. 3p + -1q + q = 0 + q Combine like terms: -1q + q = 0 3p + 0 = 0 + q 3p = 0 + q Remove the zero: 3p = q Divide each side by '3'. p = 0.3333333333q Simplifying p = 0.3333333333qSolution
p = {3q, 0.3333333333q}
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