What is the general solution for 4tan^2(θ)+tan(θ)=-4tan(θ)-1 ?

The general solution for 4tan^2(θ)+tan(θ)=-4tan(θ)-1 is θ=-0.24497…+pin,θ=(3pi)/4+pin

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4tan^2(θ)+tan(θ)=-4tan(θ)-1

4 tan^{2} (θ) + tan (θ) = - 4 tan (θ) - 1

θ = - 0.24497 \dots + πn, θ = \frac{3 π}{4} + πn

Solution steps

4 tan^{2} (θ) + tan (θ) = - 4 tan (θ) - 1

Solve by substitution

tan (θ) = - \frac{1}{4}, tan (θ) = - 1

tan (θ) = - \frac{1}{4} : θ = arctan (- \frac{1}{4}) + πn

tan (θ) = - 1 : θ = \frac{3 π}{4} + πn

Combine all the solutions

θ = arctan (- \frac{1}{4}) + πn, θ = \frac{3 π}{4} + πn

Show solutions in decimal form

θ = - 0.24497 \dots + πn, θ = \frac{3 π}{4} + πn

8 cos (c) + 6 = 3 cos (c) + 7

2 csc (A) - 4 = 0

7 tan^{2} (x) - 21 = 0

- 4 cos (x) = - sin^{2} (x) + 4

sin (x) cos (x) + sin (x) = 0

What is the general solution for 4tan^2(θ)+tan(θ)=-4tan(θ)-1 ?
The general solution for 4tan^2(θ)+tan(θ)=-4tan(θ)-1 is θ=-0.24497…+pin,θ=(3pi)/4+pin