What is the general solution for tan^2(x)+4tan(x)+2=0 ?

The general solution for tan^2(x)+4tan(x)+2=0 is x=-0.52990…+pin,x=-1.28587…+pin

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tan^2(x)+4tan(x)+2=0

tan^{2} (x) + 4 tan (x) + 2 = 0

x = - 0.52990 \dots + πn, x = - 1.28587 \dots + πn

Solution steps

tan^{2} (x) + 4 tan (x) + 2 = 0

Solve by substitution

tan (x) = - 2 + 2, tan (x) = - 2 - 2

tan (x) = - 2 + 2 : x = arctan (- 2 + 2) + πn

tan (x) = - 2 - 2 : x = arctan (- 2 - 2) + πn

Combine all the solutions

x = arctan (- 2 + 2) + πn, x = arctan (- 2 - 2) + πn

Show solutions in decimal form

x = - 0.52990 \dots + πn, x = - 1.28587 \dots + πn

- 9 sin^{2} (θ) + 4 = 5 cos (θ) - 1

tan (θ) = 1.25

6 sec (θ) + 6 = 0

2 sin (θ) - 2 = 0

- 3 sin (θ) + 3 = 2 cos^{2} (θ)

What is the general solution for tan^2(x)+4tan(x)+2=0 ?
The general solution for tan^2(x)+4tan(x)+2=0 is x=-0.52990…+pin,x=-1.28587…+pin