What is the general solution for tan^2(θ)+8tan(θ)+6=0 ?

The general solution for tan^2(θ)+8tan(θ)+6=0 is θ=-0.69732…+pin,θ=-1.43207…+pin

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tan^2(θ)+8tan(θ)+6=0

tan^{2} (θ) + 8 tan (θ) + 6 = 0

θ = - 0.69732 \dots + πn, θ = - 1.43207 \dots + πn

Solution steps

tan^{2} (θ) + 8 tan (θ) + 6 = 0

Solve by substitution

tan (θ) = - 4 + 10, tan (θ) = - 4 - 10

tan (θ) = - 4 + 10 : θ = arctan (- 4 + 10) + πn

tan (θ) = - 4 - 10 : θ = arctan (- 4 - 10) + πn

Combine all the solutions

θ = arctan (- 4 + 10) + πn, θ = arctan (- 4 - 10) + πn

Show solutions in decimal form

θ = - 0.69732 \dots + πn, θ = - 1.43207 \dots + πn

3 - sin (θ) = 5 sin (θ)

sin (x) + sin (2 x) = 0, 0 \leq x \leq 2 π

8 sin (2 x) = 16 cos (x)

3 arccos (x) = π

3 sin (2 x) - 2 sin (2 x) = 0

What is the general solution for tan^2(θ)+8tan(θ)+6=0 ?
The general solution for tan^2(θ)+8tan(θ)+6=0 is θ=-0.69732…+pin,θ=-1.43207…+pin