What is the general solution for 2cos^2(x)+9cos(x)=4 ?

The general solution for 2cos^2(x)+9cos(x)=4 is x=1.15104…+2pin,x=2pi-1.15104…+2pin

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2cos^2(x)+9cos(x)=4

2 cos^{2} (x) + 9 cos (x) = 4

x = 1.15104 \dots + 2 πn, x = 2 π - 1.15104 \dots + 2 πn

Solution steps

2 cos^{2} (x) + 9 cos (x) = 4

Solve by substitution

cos (x) = \frac{- 9 + 113}{4}, cos (x) = \frac{- 9 - 113}{4}

cos (x) = \frac{- 9 + 113}{4} : x = arccos (\frac{- 9 + 113}{4}) + 2 πn, x = 2 π - arccos (\frac{- 9 + 113}{4}) + 2 πn

cos (x) = \frac{- 9 - 113}{4} :

No Solution

Combine all the solutions

x = arccos (\frac{- 9 + 113}{4}) + 2 πn, x = 2 π - arccos (\frac{- 9 + 113}{4}) + 2 πn

Show solutions in decimal form

x = 1.15104 \dots + 2 πn, x = 2 π - 1.15104 \dots + 2 πn

sin^{2} (x) - 2 = sin (x), - x \leq x \leq 2 π

sin (2 x + 60) = \frac{1}{2}, - 18 0^{\circ} \leq, x \leq 18 0^{\circ}

80 = arcsin (\frac{1.5}{x})

sin (x) = - 0.12

tan (θ) = \frac{3}{4}, 0 \leq θ < \frac{π}{2}

What is the general solution for 2cos^2(x)+9cos(x)=4 ?
The general solution for 2cos^2(x)+9cos(x)=4 is x=1.15104…+2pin,x=2pi-1.15104…+2pin