SOLUTION: Solve for x and state any restrictions. 0° ≤ x ≤ 360° {{{ 27(3^(2tanx)) - 242(3^tanx) - 9 = 0 }}}

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Question 1187454: Solve for x and state any restrictions. 0° ≤ x ≤ 360°
+27%283%5E%282tanx%29%29+-+242%283%5Etanx%29+-+9+=+0+
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x and state any restrictions. 0° ≤ x ≤ 360°
+27%283%5E%282tanx%29%29+-+242%283%5Etanx%29+-+9+=+0+
------------------
Sub z for 3^tan(x)
-----
27z^2 - 242z - 9 = 0
(27z + 1)*(z - 9) = 0
---
z = 9
3^tan(x) = 9
tan(X) = 2
====================
27z + 1 = 0
x = -1/27
tan(x) = -1/27
==========================

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve for x and state any restrictions. 0° ≤ x ≤ 360°
+27%283%5E%282tanx%29%29+-+242%283%5Etanx%29+-+9+=+0+
------------------


            I came to fix error in the post by  Alan.


Sub z for 3^tan(x)
-----

27z^2 - 242z - 9 = 0
(27z + 1)*(z - 9) = 0

---

z = 9
3^tan(x) = 9
tan(X) = 2

====================

27z + 1 = 0
z = -1/27
3%5Etan%28x%29 = -1/27

There is no solution:  the left side is  ALWAYS  positive,  while the right side is  NEGATIVE.
==========================

ANSWER. x = arctan(2).


Solved.