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Simplifying 6p2x2 + -19pqx + 10q2 = 0 Reorder the terms: -19pqx + 6p2x2 + 10q2 = 0 Solving -19pqx + 6p2x2 + 10q2 = 0 Solving for variable 'p'. Factor a trinomial. (2px + -5q)(3px + -2q) = 0Subproblem 1
Set the factor '(2px + -5q)' equal to zero and attempt to solve: Simplifying 2px + -5q = 0 Solving 2px + -5q = 0 Move all terms containing p to the left, all other terms to the right. Add '5q' to each side of the equation. 2px + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 2px + 0 = 0 + 5q 2px = 0 + 5q Remove the zero: 2px = 5q Divide each side by '2x'. p = 2.5qx-1 Simplifying p = 2.5qx-1Subproblem 2
Set the factor '(3px + -2q)' equal to zero and attempt to solve: Simplifying 3px + -2q = 0 Solving 3px + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. 3px + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 3px + 0 = 0 + 2q 3px = 0 + 2q Remove the zero: 3px = 2q Divide each side by '3x'. p = 0.6666666667qx-1 Simplifying p = 0.6666666667qx-1Solution
p = {2.5qx-1, 0.6666666667qx-1}
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