What is the general solution for tan^2(x)+5tan(x)+6=0 ?

The general solution for tan^2(x)+5tan(x)+6=0 is x=-1.10714…+pin,x=-1.24904…+pin

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tan^2(x)+5tan(x)+6=0

tan^{2} (x) + 5 tan (x) + 6 = 0

x = - 1.10714 \dots + πn, x = - 1.24904 \dots + πn

Solution steps

tan^{2} (x) + 5 tan (x) + 6 = 0

Solve by substitution

tan (x) = - 2, tan (x) = - 3

tan (x) = - 2 : x = arctan (- 2) + πn

tan (x) = - 3 : x = arctan (- 3) + πn

Combine all the solutions

x = arctan (- 2) + πn, x = arctan (- 3) + πn

Show solutions in decimal form

x = - 1.10714 \dots + πn, x = - 1.24904 \dots + πn

cos^{4} (x) - sin^{4} (x) = 1

4 sec^{2} (x) tan (x) = 8 tan (x)

sin (x) (sin (x) - 1) = 0

tan (2 x) = tan (x)

tan^{2} (x) = - 1

What is the general solution for tan^2(x)+5tan(x)+6=0 ?
The general solution for tan^2(x)+5tan(x)+6=0 is x=-1.10714…+pin,x=-1.24904…+pin