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Simplifying 12p2 + 12q2 + -26pq = 0 Reorder the terms: -26pq + 12p2 + 12q2 = 0 Solving -26pq + 12p2 + 12q2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13pq + 6p2 + 6q2) = 0 Factor a trinomial. 2((2p + -3q)(3p + -2q)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2p + -3q)' equal to zero and attempt to solve: Simplifying 2p + -3q = 0 Solving 2p + -3q = 0 Move all terms containing p to the left, all other terms to the right. Add '3q' to each side of the equation. 2p + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 2p + 0 = 0 + 3q 2p = 0 + 3q Remove the zero: 2p = 3q Divide each side by '2'. p = 1.5q Simplifying p = 1.5qSubproblem 2
Set the factor '(3p + -2q)' equal to zero and attempt to solve: Simplifying 3p + -2q = 0 Solving 3p + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. 3p + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 3p + 0 = 0 + 2q 3p = 0 + 2q Remove the zero: 3p = 2q Divide each side by '3'. p = 0.6666666667q Simplifying p = 0.6666666667qSolution
p = {1.5q, 0.6666666667q}
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