What is the general solution for 2cos^2(x)-7cos(x)=3 ?

The general solution for 2cos^2(x)-7cos(x)=3 is x=1.96708…+2pin,x=-1.96708…+2pin

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2cos^2(x)-7cos(x)=3

2 cos^{2} (x) - 7 cos (x) = 3

x = 1.96708 \dots + 2 πn, x = - 1.96708 \dots + 2 πn

Solution steps

2 cos^{2} (x) - 7 cos (x) = 3

Solve by substitution

cos (x) = \frac{7 + 73}{4}, cos (x) = \frac{7 - 73}{4}

cos (x) = \frac{7 + 73}{4} :

No Solution

cos (x) = \frac{7 - 73}{4} : x = arccos (\frac{7 - 73}{4}) + 2 πn, x = - arccos (\frac{7 - 73}{4}) + 2 πn

Combine all the solutions

x = arccos (\frac{7 - 73}{4}) + 2 πn, x = - arccos (\frac{7 - 73}{4}) + 2 πn

Show solutions in decimal form

x = 1.96708 \dots + 2 πn, x = - 1.96708 \dots + 2 πn

tan (x) = tan (2 x)

2 cos (x) = \frac{1}{2}

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

cos (x) + 0.65 = 0

sin^{2} (x) = 0.12

What is the general solution for 2cos^2(x)-7cos(x)=3 ?
The general solution for 2cos^2(x)-7cos(x)=3 is x=1.96708…+2pin,x=-1.96708…+2pin