What is the general solution for tan^2(x)+9tan(x)+1=0 ?

The general solution for tan^2(x)+9tan(x)+1=0 is x=-0.11204…+pin,x=-1.45874…+pin

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tan^2(x)+9tan(x)+1=0

tan^{2} (x) + 9 tan (x) + 1 = 0

x = - 0.11204 \dots + πn, x = - 1.45874 \dots + πn

Solution steps

tan^{2} (x) + 9 tan (x) + 1 = 0

Solve by substitution

tan (x) = \frac{- 9 + 77}{2}, tan (x) = \frac{- 9 - 77}{2}

tan (x) = \frac{- 9 + 77}{2} : x = arctan (\frac{- 9 + 77}{2}) + πn

tan (x) = \frac{- 9 - 77}{2} : x = arctan (\frac{- 9 - 77}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 9 + 77}{2}) + πn, x = arctan (\frac{- 9 - 77}{2}) + πn

Show solutions in decimal form

x = - 0.11204 \dots + πn, x = - 1.45874 \dots + πn

sinh (t) = 0

9 sin (x) - 4 = 0

cos (2 x) \cdot 2 - 1 = 0

sec^{2} (x) + sec (x) - 6 = 0

4 + 3 sin (θ) = 0

What is the general solution for tan^2(x)+9tan(x)+1=0 ?
The general solution for tan^2(x)+9tan(x)+1=0 is x=-0.11204…+pin,x=-1.45874…+pin