What is the general solution for 6-4cos^2(x)-5cos(x)=0 ?

The general solution for 6-4cos^2(x)-5cos(x)=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin

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6-4cos^2(x)-5cos(x)=0

6 - 4 cos^{2} (x) - 5 cos (x) = 0

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

Solution steps

6 - 4 cos^{2} (x) - 5 cos (x) = 0

Solve by substitution

cos (x) = - 2, cos (x) = \frac{3}{4}

cos (x) = - 2 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn

cos (x) = \frac{32}{34.54}

tan (a) = \frac{51}{140}

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

sin (x) cot (x) csc (x) = 2

cos (2 x) + 4 cos (x) = - 3

What is the general solution for 6-4cos^2(x)-5cos(x)=0 ?
The general solution for 6-4cos^2(x)-5cos(x)=0 is x=0.72273…+2pin,x=2pi-0.72273…+2pin