What is the general solution for tan^2(θ)+5tan(θ)+6=0 ?

The general solution for tan^2(θ)+5tan(θ)+6=0 is θ=-1.10714…+pin,θ=-1.24904…+pin

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tan^2(θ)+5tan(θ)+6=0

tan^{2} (θ) + 5 tan (θ) + 6 = 0

θ = - 1.10714 \dots + πn, θ = - 1.24904 \dots + πn

Solution steps

tan^{2} (θ) + 5 tan (θ) + 6 = 0

Solve by substitution

tan (θ) = - 2, tan (θ) = - 3

tan (θ) = - 2 : θ = arctan (- 2) + πn

tan (θ) = - 3 : θ = arctan (- 3) + πn

Combine all the solutions

θ = arctan (- 2) + πn, θ = arctan (- 3) + πn

Show solutions in decimal form

θ = - 1.10714 \dots + πn, θ = - 1.24904 \dots + πn

2 cos^{2} (x) - sin^{2} (x) = 1

2 cos^{2} (θ) - sin (θ) - 1 = 0

sin (t) = - 1

sin (3 x) = 1, 0 \leq x \leq 2 π

x, z = arcsin (\frac{x}{x ^{2} + y ^{2}})

What is the general solution for tan^2(θ)+5tan(θ)+6=0 ?
The general solution for tan^2(θ)+5tan(θ)+6=0 is θ=-1.10714…+pin,θ=-1.24904…+pin