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Simplifying 10p2 + 25pq + -15q2 = 0 Reorder the terms: 25pq + 10p2 + -15q2 = 0 Solving 25pq + 10p2 + -15q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(5pq + 2p2 + -3q2) = 0 Factor a trinomial. 5((2p + -1q)(p + 3q)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2p + -1q)' equal to zero and attempt to solve: Simplifying 2p + -1q = 0 Solving 2p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. 2p + -1q + q = 0 + q Combine like terms: -1q + q = 0 2p + 0 = 0 + q 2p = 0 + q Remove the zero: 2p = q Divide each side by '2'. p = 0.5q Simplifying p = 0.5qSubproblem 2
Set the factor '(p + 3q)' equal to zero and attempt to solve: Simplifying p + 3q = 0 Solving p + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. p + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 p + 0 = 0 + -3q p = 0 + -3q Remove the zero: p = -3q Simplifying p = -3qSolution
p = {0.5q, -3q}
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