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Simplifying 3p2 + -2pq + -5q2 = 0 Reorder the terms: -2pq + 3p2 + -5q2 = 0 Solving -2pq + 3p2 + -5q2 = 0 Solving for variable 'p'. Factor a trinomial. (3p + -5q)(p + q) = 0Subproblem 1
Set the factor '(3p + -5q)' equal to zero and attempt to solve: Simplifying 3p + -5q = 0 Solving 3p + -5q = 0 Move all terms containing p to the left, all other terms to the right. Add '5q' to each side of the equation. 3p + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 3p + 0 = 0 + 5q 3p = 0 + 5q Remove the zero: 3p = 5q Divide each side by '3'. p = 1.666666667q Simplifying p = 1.666666667qSubproblem 2
Set the factor '(p + q)' equal to zero and attempt to solve: Simplifying p + q = 0 Solving p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 p + 0 = 0 + -1q p = 0 + -1q Remove the zero: p = -1q Simplifying p = -1qSolution
p = {1.666666667q, -1q}
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