If tan^(2)x = 4 - 2tanx, then tanx =

  tan(x) = -1 ±√5

Step-by-step explanation:

This is a quadratic equation in tan(x). Let z = tan(x). Then the equation is ...

  z² = 4 - 2z

  z² +2z = 4 . . . . . . . add 2z

  z² + 2z + 1 = 5 . . . . add 1 to complete the square

  (z +1)² = 5 . . . . . . . . write as a square

  z +1 = ±√5 . . . . . . . square root

  z = -1 ±√5 = tan(x) . . . . . subtract 1; use definition of z

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

answer: -0.5 would be the most likley outcome

step-by-step explanation: