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

The general solution for 2cos^2(x)+3cos(x)-3=0 is x=0.81462…+2pin,x=2pi-0.81462…+2pin

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2cos^2(x)+3cos(x)-3=0

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

x = 0.81462 \dots + 2 πn, x = 2 π - 0.81462 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{- 3 + 33}{4}, cos (x) = \frac{- 3 - 33}{4}

cos (x) = \frac{- 3 + 33}{4} : x = arccos (\frac{- 3 + 33}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 33}{4}) + 2 πn

cos (x) = \frac{- 3 - 33}{4} :

No Solution

Combine all the solutions

x = arccos (\frac{- 3 + 33}{4}) + 2 πn, x = 2 π - arccos (\frac{- 3 + 33}{4}) + 2 πn

Show solutions in decimal form

x = 0.81462 \dots + 2 πn, x = 2 π - 0.81462 \dots + 2 πn

3 sin (x) - 5 cos (x) = 0

sin^{2} (x) = 0.85

cos (x - 6 0^{\circ}) = \frac{3}{2}

(0.5 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

x, 0 = - sin (2 x) - 2 cos (x)

What is the general solution for 2cos^2(x)+3cos(x)-3=0 ?
The general solution for 2cos^2(x)+3cos(x)-3=0 is x=0.81462…+2pin,x=2pi-0.81462…+2pin