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Simplifying 42q2 + 17qd + -15d2 = 0 Reorder the terms: 17dq + -15d2 + 42q2 = 0 Solving 17dq + -15d2 + 42q2 = 0 Solving for variable 'd'. Factor a trinomial. (-5d + -6q)(3d + -7q) = 0Subproblem 1
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 = -1.2qSubproblem 2
Set the factor '(3d + -7q)' equal to zero and attempt to solve: Simplifying 3d + -7q = 0 Solving 3d + -7q = 0 Move all terms containing d to the left, all other terms to the right. Add '7q' to each side of the equation. 3d + -7q + 7q = 0 + 7q Combine like terms: -7q + 7q = 0 3d + 0 = 0 + 7q 3d = 0 + 7q Remove the zero: 3d = 7q Divide each side by '3'. d = 2.333333333q Simplifying d = 2.333333333qSolution
d = {-1.2q, 2.333333333q}
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