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Simplifying t2 + 9td + 20d2 = 0 Reorder the terms: 9dt + 20d2 + t2 = 0 Solving 9dt + 20d2 + t2 = 0 Solving for variable 'd'. Factor a trinomial. (5d + t)(4d + t) = 0Subproblem 1
Set the factor '(5d + t)' equal to zero and attempt to solve: Simplifying 5d + t = 0 Solving 5d + t = 0 Move all terms containing d to the left, all other terms to the right. Add '-1t' to each side of the equation. 5d + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 5d + 0 = 0 + -1t 5d = 0 + -1t Remove the zero: 5d = -1t Divide each side by '5'. d = -0.2t Simplifying d = -0.2tSubproblem 2
Set the factor '(4d + t)' equal to zero and attempt to solve: Simplifying 4d + t = 0 Solving 4d + t = 0 Move all terms containing d to the left, all other terms to the right. Add '-1t' to each side of the equation. 4d + t + -1t = 0 + -1t Combine like terms: t + -1t = 0 4d + 0 = 0 + -1t 4d = 0 + -1t Remove the zero: 4d = -1t Divide each side by '4'. d = -0.25t Simplifying d = -0.25tSolution
d = {-0.2t, -0.25t}
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