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Find the positive difference between the solutions to the equation 6t^2 + 30 = 41t  + 7t - 2t^2.

 Feb 19, 2022
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6t2 + 30  =  41t + 7t - 2t2

 

1)  Simplify the right side:  6t2 + 30  =  48t - 2t2

 

2)  Get all the terms to the left side:   6t2 + 30 - 48t + 2t2  =  0

 

3)  Simplify the left side:  8t2 - 48t + 30  =  0   --->   4t2 - 24t + 15  =  0

 

4)  Use the quadratic formula to get the two solutions:

 

     x  =  [ 24 + sqrt( (-24)2 - 4(4)(15) ) ] / (2·4)  =  [ 24 + sqrt(336) ] / 8

                       =  [ 24 + 4sqrt(21) ] / 8  =  [ 6 + sqrt(21) ] / 2

 

    and  x =  [ 6 - sqrt(21) ] / 2

 

7)  Finish by subtracting the smaller solution from the larger solution.

 Feb 19, 2022

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