What is the general solution for tan^2(x)+7tan(x)+9=0 ?

The general solution for tan^2(x)+7tan(x)+9=0 is x=-1.03835…+pin,x=-1.38440…+pin

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tan^2(x)+7tan(x)+9=0

tan^{2} (x) + 7 tan (x) + 9 = 0

x = - 1.03835 \dots + πn, x = - 1.38440 \dots + πn

Solution steps

tan^{2} (x) + 7 tan (x) + 9 = 0

Solve by substitution

tan (x) = \frac{- 7 + 13}{2}, tan (x) = \frac{- 7 - 13}{2}

tan (x) = \frac{- 7 + 13}{2} : x = arctan (\frac{- 7 + 13}{2}) + πn

tan (x) = \frac{- 7 - 13}{2} : x = arctan (\frac{- 7 - 13}{2}) + πn

Combine all the solutions

x = arctan (\frac{- 7 + 13}{2}) + πn, x = arctan (\frac{- 7 - 13}{2}) + πn

Show solutions in decimal form

x = - 1.03835 \dots + πn, x = - 1.38440 \dots + πn

4 cos (x) = sec (x) + 3, 0 \leq x < 2 π

x, - \frac{1}{2 y ^{2}} = 3 sin (x) - \frac{1}{8}

sin (θ) = \frac{150 sin ( 11 5 ^{\circ} )}{212.6}

- sin (x) - sin (2 x) = 0

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

What is the general solution for tan^2(x)+7tan(x)+9=0 ?
The general solution for tan^2(x)+7tan(x)+9=0 is x=-1.03835…+pin,x=-1.38440…+pin