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Simplifying 4p2 + 3pq + -1q2 = 0 Reorder the terms: 3pq + 4p2 + -1q2 = 0 Solving 3pq + 4p2 + -1q2 = 0 Solving for variable 'p'. Factor a trinomial. (4p + -1q)(p + q) = 0Subproblem 1
Set the factor '(4p + -1q)' equal to zero and attempt to solve: Simplifying 4p + -1q = 0 Solving 4p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. 4p + -1q + q = 0 + q Combine like terms: -1q + q = 0 4p + 0 = 0 + q 4p = 0 + q Remove the zero: 4p = q Divide each side by '4'. p = 0.25q Simplifying p = 0.25qSubproblem 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 = {0.25q, -1q}
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