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Simplifying 20p2 + -100pq + 125q2 = 0 Reorder the terms: -100pq + 20p2 + 125q2 = 0 Solving -100pq + 20p2 + 125q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20pq + 4p2 + 25q2) = 0 Factor a trinomial. 5((2p + -5q)(2p + -5q)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2p + -5q)' equal to zero and attempt to solve: Simplifying 2p + -5q = 0 Solving 2p + -5q = 0 Move all terms containing p to the left, all other terms to the right. Add '5q' to each side of the equation. 2p + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 2p + 0 = 0 + 5q 2p = 0 + 5q Remove the zero: 2p = 5q Divide each side by '2'. p = 2.5q Simplifying p = 2.5qSubproblem 2
Set the factor '(2p + -5q)' equal to zero and attempt to solve: Simplifying 2p + -5q = 0 Solving 2p + -5q = 0 Move all terms containing p to the left, all other terms to the right. Add '5q' to each side of the equation. 2p + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 2p + 0 = 0 + 5q 2p = 0 + 5q Remove the zero: 2p = 5q Divide each side by '2'. p = 2.5q Simplifying p = 2.5qSolution
p = {2.5q, 2.5q}
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