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

The general solution for tan^2(θ)+6tan(θ)+8=0 is θ=-1.10714…+pin,θ=-1.32581…+pin

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tan^2(θ)+6tan(θ)+8=0

tan^{2} (θ) + 6 tan (θ) + 8 = 0

θ = - 1.10714 \dots + πn, θ = - 1.32581 \dots + πn

Solution steps

tan^{2} (θ) + 6 tan (θ) + 8 = 0

Solve by substitution

tan (θ) = - 2, tan (θ) = - 4

tan (θ) = - 2 : θ = arctan (- 2) + πn

tan (θ) = - 4 : θ = arctan (- 4) + πn

Combine all the solutions

θ = arctan (- 2) + πn, θ = arctan (- 4) + πn

Show solutions in decimal form

θ = - 1.10714 \dots + πn, θ = - 1.32581 \dots + πn

sin (\frac{x}{2}) + cos (x) = 1

- cos (x) + cos (2 x) = 0

sin (4 x) + 1 = 0

4 cos^{2} (θ) = 3

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

What is the general solution for tan^2(θ)+6tan(θ)+8=0 ?
The general solution for tan^2(θ)+6tan(θ)+8=0 is θ=-1.10714…+pin,θ=-1.32581…+pin