0.001869 = tanx + tan^2x

Solve for x please, I simplified to that from 1800 = 2500tanx - 490(1+tan^2x). I think I simplified correctly, but if not solve from the original equation please.

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           0.001869 = tanx + tan²x       ← Notice that this is a quadratic equation in tanx.
                                                              You can solve it by using the Quadratic Formula
                                                              or by completing the square.
                                                              I'll use completing the square.

           0.001869 = tan²x + tanx
0.001869 + (½)² = tan²x + tanx + (½)²            ← Added (b/2)² to complete the square
0.001869 + 0.25 = (tanx + ½)²
       (tanx + 0.5)² = 0.251869                           ← Now, take the square root of both sides
           tanx + 0.5 = ±√[0.251869]                   ← By the square root property
                    tanx = -0.5 ± √[0.251869]
                    tanx = 0.001866  or  -1.00187

So, for 0 ≤ x ≤ 2π:
x = arctan(0.001866) = 0.001866 ✔   or   (π + 0.001866) = 3.14346 ✔
OR
x = arctan(-1.00187) = -0.786332    or    (π - 0.786332)
                                2π-0.786332    or    (π - 0.786332)
                                      5.49685 ✔   or    2.35526 ✔

                                                 ANSWER
                         x ≈ 0.001866, 2.35526, 3.14346, 5.49685


Hope that helps
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