What is the general solution for 2cos^2(x)+3cos(x)=1 ?

The general solution for 2cos^2(x)+3cos(x)=1 is x=1.28619…+2pin,x=2pi-1.28619…+2pin

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

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

x = 1.28619 \dots + 2 πn, x = 2 π - 1.28619 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{- 3 + 17}{4}, cos (x) = \frac{- 3 - 17}{4}

cos (x) = \frac{- 3 + 17}{4} : x = arccos (\frac{- 3 + 17}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 17}{4}) + 2 πn

cos (x) = \frac{- 3 - 17}{4} :

No Solution

Combine all the solutions

x = arccos (\frac{- 3 + 17}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 17}{4}) + 2 πn

Show solutions in decimal form

x = 1.28619 \dots + 2 πn, x = 2 π - 1.28619 \dots + 2 πn

sin (θ) = - \frac{5}{6}, sec (θ)

sin (x) = \frac{1}{3}, cos (x)

6 - 5 tan (3 x + 1) = 26

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

(5 tan (θ) + 25) = 0

What is the general solution for 2cos^2(x)+3cos(x)=1 ?
The general solution for 2cos^2(x)+3cos(x)=1 is x=1.28619…+2pin,x=2pi-1.28619…+2pin