SOLUTION: Solve the equation 4tan^2x + 5 tanx + 1 = 0

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Question 1112878: Solve the equation 4tan^2x + 5 tanx + 1 = 0
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It's a quadratic in tan(x).
I would factor it.

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
Standard way to solve such problems is to introduce new variable


u = tan(x).


Then your equation takes the form


4u%5E2+%2B+5u+%2B+1 = 0.


You can factor left side 


(4u+1)*(u+1) = 0


and it gives you the solutions


u = -1%2F4,  u = -1.


Thus  EITHER  tan(x) = -1%2F4  ====>  x = arctan%28-1%2F4%29   OR  tan(x) = -1   and  x = arctan%28-1%29 = -45 degs.

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The advise by @Alan is right, without any doubt.

With only one notice:   The person who is able to follow to this advise,  will never come to this forum with such a question.

Since he  (or she)  will do everything on his  (or her)  own.

In other words,  this advise does not work (is useless) for a person who came to  this forum   with such a question.

Although, again,  the advise itself is absolutely correct.