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Simplifying 15p2 + 40pq + 25q2 = 0 Reorder the terms: 40pq + 15p2 + 25q2 = 0 Solving 40pq + 15p2 + 25q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(8pq + 3p2 + 5q2) = 0 Factor a trinomial. 5((p + q)(3p + 5q)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(p + q)' equal to zero and attempt to solve: Simplifying p + q = 0 Solving p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 p + 0 = 0 + -1q p = 0 + -1q Remove the zero: p = -1q Simplifying p = -1qSubproblem 2
Set the factor '(3p + 5q)' equal to zero and attempt to solve: Simplifying 3p + 5q = 0 Solving 3p + 5q = 0 Move all terms containing p to the left, all other terms to the right. Add '-5q' to each side of the equation. 3p + 5q + -5q = 0 + -5q Combine like terms: 5q + -5q = 0 3p + 0 = 0 + -5q 3p = 0 + -5q Remove the zero: 3p = -5q Divide each side by '3'. p = -1.666666667q Simplifying p = -1.666666667qSolution
p = {-1q, -1.666666667q}
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