What is the general solution for tan^2(x)+3tan(x)-10=0 ?

The general solution for tan^2(x)+3tan(x)-10=0 is x=1.10714…+pin,x=-1.37340…+pin

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tan^2(x)+3tan(x)-10=0

tan^{2} (x) + 3 tan (x) - 10 = 0

x = 1.10714 \dots + πn, x = - 1.37340 \dots + πn

Solution steps

tan^{2} (x) + 3 tan (x) - 10 = 0

Solve by substitution

tan (x) = 2, tan (x) = - 5

tan (x) = 2 : x = arctan (2) + πn

tan (x) = - 5 : x = arctan (- 5) + πn

Combine all the solutions

x = arctan (2) + πn, x = arctan (- 5) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = - 1.37340 \dots + πn

cos^{2} (x) - sin (x) = - 1

4 sin (x) - 3 sin^{2} (x) + cos^{2} (x) - 2 = 0

cos^{2} (x) + 3 cos (x) = 1

cot^{2} (x) = \frac{tan ( x )}{2}

tan (θ) = \frac{3.2}{4.1}

What is the general solution for tan^2(x)+3tan(x)-10=0 ?
The general solution for tan^2(x)+3tan(x)-10=0 is x=1.10714…+pin,x=-1.37340…+pin