What is the general solution for tan^2(θ)+7tan(θ)+8=0 ?

The general solution for tan^2(θ)+7tan(θ)+8=0 is θ=-0.96330…+pin,θ=-1.39289…+pin

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tan^2(θ)+7tan(θ)+8=0

tan^{2} (θ) + 7 tan (θ) + 8 = 0

θ = - 0.96330 \dots + πn, θ = - 1.39289 \dots + πn

Solution steps

tan^{2} (θ) + 7 tan (θ) + 8 = 0

Solve by substitution

tan (θ) = \frac{- 7 + 17}{2}, tan (θ) = \frac{- 7 - 17}{2}

tan (θ) = \frac{- 7 + 17}{2} : θ = arctan (\frac{- 7 + 17}{2}) + πn

tan (θ) = \frac{- 7 - 17}{2} : θ = arctan (\frac{- 7 - 17}{2}) + πn

Combine all the solutions

θ = arctan (\frac{- 7 + 17}{2}) + πn, θ = arctan (\frac{- 7 - 17}{2}) + πn

Show solutions in decimal form

θ = - 0.96330 \dots + πn, θ = - 1.39289 \dots + πn

cos (4 x) = \frac{2}{3}

- 1 + cos (θ) = cos (2 θ)

3 cos (θ) = 3 sin (- θ)

3 tan (\frac{2 x}{3}) + 1 = 0

sin (x) = \frac{11}{61}

What is the general solution for tan^2(θ)+7tan(θ)+8=0 ?
The general solution for tan^2(θ)+7tan(θ)+8=0 is θ=-0.96330…+pin,θ=-1.39289…+pin