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Simplifying 3p2 + -14pq + 8q2 = 0 Reorder the terms: -14pq + 3p2 + 8q2 = 0 Solving -14pq + 3p2 + 8q2 = 0 Solving for variable 'p'. Factor a trinomial. (p + -4q)(3p + -2q) = 0Subproblem 1
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 = 4qSubproblem 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 = {4q, 0.6666666667q}
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