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Simplifying 20q2 + -27qd + 9d2 = 0 Reorder the terms: -27dq + 9d2 + 20q2 = 0 Solving -27dq + 9d2 + 20q2 = 0 Solving for variable 'd'. Factor a trinomial. (3d + -5q)(3d + -4q) = 0Subproblem 1
Set the factor '(3d + -5q)' equal to zero and attempt to solve: Simplifying 3d + -5q = 0 Solving 3d + -5q = 0 Move all terms containing d to the left, all other terms to the right. Add '5q' to each side of the equation. 3d + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 3d + 0 = 0 + 5q 3d = 0 + 5q Remove the zero: 3d = 5q Divide each side by '3'. d = 1.666666667q Simplifying d = 1.666666667qSubproblem 2
Set the factor '(3d + -4q)' equal to zero and attempt to solve: Simplifying 3d + -4q = 0 Solving 3d + -4q = 0 Move all terms containing d to the left, all other terms to the right. Add '4q' to each side of the equation. 3d + -4q + 4q = 0 + 4q Combine like terms: -4q + 4q = 0 3d + 0 = 0 + 4q 3d = 0 + 4q Remove the zero: 3d = 4q Divide each side by '3'. d = 1.333333333q Simplifying d = 1.333333333qSolution
d = {1.666666667q, 1.333333333q}
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