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Simplifying t2 + 5td + -24d2 = 0 Reorder the terms: 5dt + -24d2 + t2 = 0 Solving 5dt + -24d2 + t2 = 0 Solving for variable 'd'. Factor a trinomial. (-8d + -1t)(3d + -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 '(3d + -1t)' equal to zero and attempt to solve: Simplifying 3d + -1t = 0 Solving 3d + -1t = 0 Move all terms containing d to the left, all other terms to the right. Add 't' to each side of the equation. 3d + -1t + t = 0 + t Combine like terms: -1t + t = 0 3d + 0 = 0 + t 3d = 0 + t Remove the zero: 3d = t Divide each side by '3'. d = 0.3333333333t Simplifying d = 0.3333333333tSolution
d = {-0.125t, 0.3333333333t}
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