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Simplifying p2q2 + -6pq + 8 = 0 Reorder the terms: 8 + -6pq + p2q2 = 0 Solving 8 + -6pq + p2q2 = 0 Solving for variable 'p'. Factor a trinomial. (2 + -1pq)(4 + -1pq) = 0Subproblem 1
Set the factor '(2 + -1pq)' equal to zero and attempt to solve: Simplifying 2 + -1pq = 0 Solving 2 + -1pq = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1pq = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1pq = 0 + -2 -1pq = 0 + -2 Combine like terms: 0 + -2 = -2 -1pq = -2 Divide each side by '-1q'. p = 2q-1 Simplifying p = 2q-1Subproblem 2
Set the factor '(4 + -1pq)' equal to zero and attempt to solve: Simplifying 4 + -1pq = 0 Solving 4 + -1pq = 0 Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1pq = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1pq = 0 + -4 -1pq = 0 + -4 Combine like terms: 0 + -4 = -4 -1pq = -4 Divide each side by '-1q'. p = 4q-1 Simplifying p = 4q-1Solution
p = {2q-1, 4q-1}
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