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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

cos (x) = - 2 :

No Solution

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

3 cos (2 θ) = - 3 cos (θ)

csc^{2} (θ) + 3 csc (θ) + 2 = 0

cos^{2} (x) = 3 - 5 sin (x)

cos^{2} (θ) - sin^{2} (θ) = - 1

8 sin (\frac{x}{2}) + 8 cos (x) = 0

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