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Simplifying p(p + q) + 2p(p + -1q) = 0 (p * p + q * p) + 2p(p + -1q) = 0 Reorder the terms: (pq + p2) + 2p(p + -1q) = 0 (pq + p2) + 2p(p + -1q) = 0 pq + p2 + (p * 2p + -1q * 2p) = 0 Reorder the terms: pq + p2 + (-2pq + 2p2) = 0 pq + p2 + (-2pq + 2p2) = 0 Reorder the terms: pq + -2pq + p2 + 2p2 = 0 Combine like terms: pq + -2pq = -1pq -1pq + p2 + 2p2 = 0 Combine like terms: p2 + 2p2 = 3p2 -1pq + 3p2 = 0 Solving -1pq + 3p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-1q + 3p) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-1q + 3p)' equal to zero and attempt to solve: Simplifying -1q + 3p = 0 Reorder the terms: 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 = {0, 0.3333333333q}
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