What is the general solution for tan^2(x)+5tan(x)-1=0 ?

The general solution for tan^2(x)+5tan(x)-1=0 is x=0.19025…+pin,x=-1.38054…+pin

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tan^2(x)+5tan(x)-1=0

tan^{2} (x) + 5 tan (x) - 1 = 0

x = 0.19025 \dots + πn, x = - 1.38054 \dots + πn

Solution steps

tan^{2} (x) + 5 tan (x) - 1 = 0

Solve by substitution

tan (x) = \frac{- 5 + 29}{2}, tan (x) = \frac{- 5 - 29}{2}

tan (x) = \frac{- 5 + 29}{2} : x = arctan (\frac{- 5 + 29}{2}) + πn

tan (x) = \frac{- 5 - 29}{2} : x = arctan (\frac{- 5 - 29}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 5 + 29}{2}) + πn, x = arctan (\frac{- 5 - 29}{2}) + πn

Show solutions in decimal form

x = 0.19025 \dots + πn, x = - 1.38054 \dots + πn

csc (θ) + 1 = 0

2 sin^{2} (θ) - 3 sin (θ) + 1 = 0, 0 \leq θ \leq 2 π

2 sec (x) + 2 tan (x) = 2

2 sin^{2} (θ) + 3 sin (θ) = 0

cos^{2} (x) = sin^{2} (\frac{x}{2})

What is the general solution for tan^2(x)+5tan(x)-1=0 ?
The general solution for tan^2(x)+5tan(x)-1=0 is x=0.19025…+pin,x=-1.38054…+pin