SOLUTION: I need to solve this equation for the interval [0, 2pi) : -tan^2(x)+3 = 2tanx+4

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Question 1063374: I need to solve this equation for the interval [0, 2pi) :
-tan^2(x)+3 = 2tanx+4
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
tan^2 x+2 tan x+1=0, by moving terms.
(tan x +1)^2=0
tan x=-1
tan x=3 pi/4, 7 pi/4
-1+3=-2+4, check

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
I need to solve this equation for the interval [0, 2pi) :
-tan^2(x)+3 = 2tanx+4
~~~~~~~~~~~~~~~~~~ 

-tan%5E2%28x%29%2B3 = 2tanx + 4   --->  

tan%5E2%28x%29+%2B+2tan%28x%29+%2B+1 = 0  --->

%28tan%28x%29+%2B+1%29%5E2 = 0  --->

tan(x) + 1 = 0  --->  tan(x) = -1   --->  x = 3pi%2F4  and/or  x = 7pi%2F4.

Answer.  There are two solutions  x = 3pi%2F4  and/or  x = 7pi%2F4.