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Simplifying 12q2 + 11qd + -15d2 = 0 Reorder the terms: 11dq + -15d2 + 12q2 = 0 Solving 11dq + -15d2 + 12q2 = 0 Solving for variable 'd'. Factor a trinomial. (-5d + -3q)(3d + -4q) = 0Subproblem 1
Set the factor '(-5d + -3q)' equal to zero and attempt to solve: Simplifying -5d + -3q = 0 Solving -5d + -3q = 0 Move all terms containing d to the left, all other terms to the right. Add '3q' to each side of the equation. -5d + -3q + 3q = 0 + 3q Combine like terms: -3q + 3q = 0 -5d + 0 = 0 + 3q -5d = 0 + 3q Remove the zero: -5d = 3q Divide each side by '-5'. d = -0.6q Simplifying d = -0.6qSubproblem 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 = {-0.6q, 1.333333333q}
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