What is the general solution for tan^2(x)-5tan(x)-9=0 ?

The general solution for tan^2(x)-5tan(x)-9=0 is x=1.41592…+pin,x=-0.95227…+pin

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tan^2(x)-5tan(x)-9=0

tan^{2} (x) - 5 tan (x) - 9 = 0

x = 1.41592 \dots + πn, x = - 0.95227 \dots + πn

Solution steps

tan^{2} (x) - 5 tan (x) - 9 = 0

Solve by substitution

tan (x) = \frac{5 + 61}{2}, tan (x) = \frac{5 - 61}{2}

tan (x) = \frac{5 + 61}{2} : x = arctan (\frac{5 + 61}{2}) + πn

tan (x) = \frac{5 - 61}{2} : x = arctan (\frac{5 - 61}{2}) + πn

Combine all the solutions

x = arctan (\frac{5 + 61}{2}) + πn, x = arctan (\frac{5 - 61}{2}) + πn

Show solutions in decimal form

x = 1.41592 \dots + πn, x = - 0.95227 \dots + πn

arctan (t) = \frac{π}{4}

tan (\frac{π}{2} - θ) = cos (- θ)

tan (x) = - \frac{24}{7}

sin^{3} (x) + sin (x) = 0

x, sin (x) = - \frac{1}{2}

What is the general solution for tan^2(x)-5tan(x)-9=0 ?
The general solution for tan^2(x)-5tan(x)-9=0 is x=1.41592…+pin,x=-0.95227…+pin