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Simplifying -14p2 + 21pq + 14q2 = 0 Reorder the terms: 21pq + -14p2 + 14q2 = 0 Solving 21pq + -14p2 + 14q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '7'. 7(3pq + -2p2 + 2q2) = 0 Factor a trinomial. 7((-2p + -1q)(p + -2q)) = 0 Ignore the factor 7.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 + -2q)' equal to zero and attempt to solve: Simplifying p + -2q = 0 Solving p + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. p + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 p + 0 = 0 + 2q p = 0 + 2q Remove the zero: p = 2q Simplifying p = 2qSolution
p = {-0.5q, 2q}
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