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Simplifying 10p2 + -5pq + -180q2 = 0 Reorder the terms: -5pq + 10p2 + -180q2 = 0 Solving -5pq + 10p2 + -180q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1pq + 2p2 + -36q2) = 0 Factor a trinomial. 5((2p + -9q)(p + 4q)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2p + -9q)' equal to zero and attempt to solve: Simplifying 2p + -9q = 0 Solving 2p + -9q = 0 Move all terms containing p to the left, all other terms to the right. Add '9q' to each side of the equation. 2p + -9q + 9q = 0 + 9q Combine like terms: -9q + 9q = 0 2p + 0 = 0 + 9q 2p = 0 + 9q Remove the zero: 2p = 9q Divide each side by '2'. p = 4.5q Simplifying p = 4.5qSubproblem 2
Set the factor '(p + 4q)' equal to zero and attempt to solve: Simplifying p + 4q = 0 Solving p + 4q = 0 Move all terms containing p to the left, all other terms to the right. Add '-4q' to each side of the equation. p + 4q + -4q = 0 + -4q Combine like terms: 4q + -4q = 0 p + 0 = 0 + -4q p = 0 + -4q Remove the zero: p = -4q Simplifying p = -4qSolution
p = {4.5q, -4q}
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