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Simplifying t2 + 4td + -32d2 = 0 Reorder the terms: 4dt + -32d2 + t2 = 0 Solving 4dt + -32d2 + t2 = 0 Solving for variable 'd'. Factor a trinomial. (-8d + -1t)(4d + -1t) = 0Subproblem 1
Set the factor '(-8d + -1t)' equal to zero and attempt to solve: Simplifying -8d + -1t = 0 Solving -8d + -1t = 0 Move all terms containing d to the left, all other terms to the right. Add 't' to each side of the equation. -8d + -1t + t = 0 + t Combine like terms: -1t + t = 0 -8d + 0 = 0 + t -8d = 0 + t Remove the zero: -8d = t Divide each side by '-8'. d = -0.125t Simplifying d = -0.125tSubproblem 2
Set the factor '(4d + -1t)' equal to zero and attempt to solve: Simplifying 4d + -1t = 0 Solving 4d + -1t = 0 Move all terms containing d to the left, all other terms to the right. Add 't' to each side of the equation. 4d + -1t + t = 0 + t Combine like terms: -1t + t = 0 4d + 0 = 0 + t 4d = 0 + t Remove the zero: 4d = t Divide each side by '4'. d = 0.25t Simplifying d = 0.25tSolution
d = {-0.125t, 0.25t}
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