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Simplifying p2 + -6pq + 5q2 = 0 Reorder the terms: -6pq + p2 + 5q2 = 0 Solving -6pq + p2 + 5q2 = 0 Solving for variable 'p'. Factor a trinomial. (p + -5q)(p + -1q) = 0Subproblem 1
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 = 5qSubproblem 2
Set the factor '(p + -1q)' equal to zero and attempt to solve: Simplifying p + -1q = 0 Solving p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. p + -1q + q = 0 + q Combine like terms: -1q + q = 0 p + 0 = 0 + q p = 0 + q Remove the zero: p = q Simplifying p = qSolution
p = {5q, q}
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