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Simplifying 30q2 + 17qd + -35d2 = 0 Reorder the terms: 17dq + -35d2 + 30q2 = 0 Solving 17dq + -35d2 + 30q2 = 0 Solving for variable 'd'. Factor a trinomial. (-7d + -5q)(5d + -6q) = 0Subproblem 1
Set the factor '(-7d + -5q)' equal to zero and attempt to solve: Simplifying -7d + -5q = 0 Solving -7d + -5q = 0 Move all terms containing d to the left, all other terms to the right. Add '5q' to each side of the equation. -7d + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 -7d + 0 = 0 + 5q -7d = 0 + 5q Remove the zero: -7d = 5q Divide each side by '-7'. d = -0.7142857143q Simplifying d = -0.7142857143qSubproblem 2
Set the factor '(5d + -6q)' equal to zero and attempt to solve: Simplifying 5d + -6q = 0 Solving 5d + -6q = 0 Move all terms containing d to the left, all other terms to the right. Add '6q' to each side of the equation. 5d + -6q + 6q = 0 + 6q Combine like terms: -6q + 6q = 0 5d + 0 = 0 + 6q 5d = 0 + 6q Remove the zero: 5d = 6q Divide each side by '5'. d = 1.2q Simplifying d = 1.2qSolution
d = {-0.7142857143q, 1.2q}
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