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Simplifying -15p2 + 72pq + 15q2 = 0 Reorder the terms: 72pq + -15p2 + 15q2 = 0 Solving 72pq + -15p2 + 15q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3'. 3(24pq + -5p2 + 5q2) = 0 Factor a trinomial. 3((-5p + -1q)(p + -5q)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5p + -1q)' equal to zero and attempt to solve: Simplifying -5p + -1q = 0 Solving -5p + -1q = 0 Move all terms containing p to the left, all other terms to the right. Add 'q' to each side of the equation. -5p + -1q + q = 0 + q Combine like terms: -1q + q = 0 -5p + 0 = 0 + q -5p = 0 + q Remove the zero: -5p = q Divide each side by '-5'. p = -0.2q Simplifying p = -0.2qSubproblem 2
Set the factor '(p + -5q)' equal to zero and attempt to solve: Simplifying p + -5q = 0 Solving p + -5q = 0 Move all terms containing p to the left, all other terms to the right. Add '5q' to each side of the equation. p + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 p + 0 = 0 + 5q p = 0 + 5q Remove the zero: p = 5q Simplifying p = 5qSolution
p = {-0.2q, 5q}
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