What is the general solution for tan^2(x)+5tan(x)-7=0 ?

The general solution for tan^2(x)+5tan(x)-7=0 is x=0.85074…+pin,x=-1.40934…+pin

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tan^2(x)+5tan(x)-7=0

tan^{2} (x) + 5 tan (x) - 7 = 0

x = 0.85074 \dots + πn, x = - 1.40934 \dots + πn

Solution steps

tan^{2} (x) + 5 tan (x) - 7 = 0

Solve by substitution

tan (x) = \frac{- 5 + 53}{2}, tan (x) = \frac{- 5 - 53}{2}

tan (x) = \frac{- 5 + 53}{2} : x = arctan (\frac{- 5 + 53}{2}) + πn

tan (x) = \frac{- 5 - 53}{2} : x = arctan (\frac{- 5 - 53}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 5 + 53}{2}) + πn, x = arctan (\frac{- 5 - 53}{2}) + πn

Show solutions in decimal form

x = 0.85074 \dots + πn, x = - 1.40934 \dots + πn

sin (x) = \frac{- 3}{4}

cot^{2} (x) - 3 cot (x) = 0

x, y = sec (x)

tan (θ) = 2

cos (a) = 0.5, tan (a) - 3

What is the general solution for tan^2(x)+5tan(x)-7=0 ?
The general solution for tan^2(x)+5tan(x)-7=0 is x=0.85074…+pin,x=-1.40934…+pin