Solve the equation for solutions over the interval ​[0​°, 360°​). tan^(2)x + 7 tanx +8 =0

Question

Solve the equation for solutions over the interval ​[0​°, 360°​).


`tan^(2)x + 7 tanx +8 =0`

Answer 1

`x=98.13^\circ,135^\circ,278.13^\circ,315^\circ`

Explanation:

`tan^2x+7tanx+8=0,[0^(\circ),360^\circ)`

`tan^2x+7tanx+8=0`

`u=tanx` <-- U-substitution

`u^2+7u+8=0`

`(u+7)(u+1)=0`

`(tanx+7)(tanx+1)=0` <-- Replace u with tanx

`tanx+7=0`

`tanx=-7`

`x=98.13^\circ,278.13^\circ`

`tanx+1=0`

`tanx=-1`

`x=135^\circ,315^\circ`

Therefore,
`x=98.13^\circ,135^\circ,278.13^\circ,315^\circ`