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

The general solution for tan^2(x)+5tan(x)+2=0 is x=-0.41320…+pin,x=-1.35498…+pin

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tan^2(x)+5tan(x)+2=0

tan^{2} (x) + 5 tan (x) + 2 = 0

x = - 0.41320 \dots + πn, x = - 1.35498 \dots + πn

Solution steps

tan^{2} (x) + 5 tan (x) + 2 = 0

Solve by substitution

tan (x) = \frac{- 5 + 17}{2}, tan (x) = \frac{- 5 - 17}{2}

tan (x) = \frac{- 5 + 17}{2} : x = arctan (\frac{- 5 + 17}{2}) + πn

tan (x) = \frac{- 5 - 17}{2} : x = arctan (\frac{- 5 - 17}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 5 + 17}{2}) + πn, x = arctan (\frac{- 5 - 17}{2}) + πn

Show solutions in decimal form

x = - 0.41320 \dots + πn, x = - 1.35498 \dots + πn

2 sin^{2} (x) + 3 cos (2 x) = 2

tan (x) = 12

2 + 3 cos^{2} (θ) = sin^{2} (θ) + 4 cos (θ)

arctan (4 x) + arctan (6 x) = \frac{π}{2}

x, y = \frac{1}{tan ( x \cdot π )}

What is the general solution for tan^2(x)+5tan(x)+2=0 ?
The general solution for tan^2(x)+5tan(x)+2=0 is x=-0.41320…+pin,x=-1.35498…+pin