Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)

Question

tan²(x) + tan(x) − 6 = 0

Answer 1

let y=tanx

y^2 +y -6=0

(y+3)(y-2)=0

y=-3 = tanx x=arctan-3 +180n where n=any integer

= about -72 +180n degrees

y=2=tanx, x=arctan2 + 180n

= about 63+180n degrees

Answer 2

The equation is a quadratic in tan(x).

Factor the Quadratic

tan²(x) + tan(x) − 6 = 0

(tan(x) + 3)(tan(x) – 2) = 0

tan(x) = –3

tan(x) = 2

Exact Solutions

x = tan⁻¹(–3) + nπ, tan⁻¹(2) + nπ

Appropriate decimal solutions

x = 1.89 + nπ, 1.11 + nπ

or

x = 0.60π + nπ, 0.35π + nπ

(I'm not sure what form of solution is sought.)