SOLUTION: (t+2)(t+2)(t-3)(t-3)=9

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Question 1084474: (t+2)(t+2)(t-3)(t-3)=9
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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Introduce new variable p = t-0.5.

Then t + 2 = (t-0.5) + 2.5 = p + 2.5,

     t - 3 = (t-0.5) - 2.5 = p - 2.5,


and your original equation takes the form 

     (p+2.5)*(p+2.5)*(p-2.5)*(p-2.5) = 9,   or

     %28p%5E2-2.5%5E2%29%5E2 = 9.


It implies  p%5E2+-+6.25 = +/-3.


1)  if p%5E2+-+6.25 = 3,  then p%5E2 = 3 + 6.25 = 9.25,  and  p = +/- {{sqrt(9.25)}}} = +/- 3.0414 (approximately, with 4 correct decimals).

                          / =  3.5414,   or
    Hence, t = p + 0.5 = |
                          \ = -2.5414.
                          


2)  if p%5E2+-+6.25 = -3,  then p%5E2 = -3 + 6.25 = 3.25,  and  p = +/- {{sqrt(3.25)}}} = +/- 1.8028 (approximately, with 4 correct decimals).

                          / =  2.3028,   or
    Hence, t = p + 0.5 = |
                          \ = -1.3028.


Answer.  There are 4 solutions for t:  3.5414,  -2.5414,  2.3028  and  -1.3028  (approximately; with 4 correct decimals).