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

The general solution for 2tan^2(x)+tan(x)-2=0 is x=0.66290…+pin,x=-0.90788…+pin

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

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

x = 0.66290 \dots + πn, x = - 0.90788 \dots + πn

Solution steps

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

Solve by substitution

tan (x) = \frac{- 1 + 17}{4}, tan (x) = \frac{- 1 - 17}{4}

tan (x) = \frac{- 1 + 17}{4} : x = arctan (\frac{- 1 + 17}{4}) + πn

tan (x) = \frac{- 1 - 17}{4} : x = arctan (\frac{- 1 - 17}{4}) + πn

Combine all the solutions

x = arctan (\frac{- 1 + 17}{4}) + πn, x = arctan (\frac{- 1 - 17}{4}) + πn

Show solutions in decimal form

x = 0.66290 \dots + πn, x = - 0.90788 \dots + πn

3 sec (θ) + 1 = 7, 0 \leq θ < 2 π

sin (A) cos (A) = sin (A)

tan (\frac{x}{2} - \frac{π}{4}) = 1

3 sin (θ) = 1

sin (A) tan (A) = sin (A)

What is the general solution for 2tan^2(x)+tan(x)-2=0 ?
The general solution for 2tan^2(x)+tan(x)-2=0 is x=0.66290…+pin,x=-0.90788…+pin