What is the general solution for 2cos^2(x)+6cos(x)=-1 ?

The general solution for 2cos^2(x)+6cos(x)=-1 is x=1.74886…+2pin,x=-1.74886…+2pin

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2cos^2(x)+6cos(x)=-1

2 cos^{2} (x) + 6 cos (x) = - 1

x = 1.74886 \dots + 2 πn, x = - 1.74886 \dots + 2 πn

Solution steps

2 cos^{2} (x) + 6 cos (x) = - 1

Solve by substitution

cos (x) = \frac{- 3 + 7}{2}, cos (x) = - \frac{3 + 7}{2}

cos (x) = \frac{- 3 + 7}{2} : x = arccos (\frac{- 3 + 7}{2}) + 2 πn, x = - arccos (\frac{- 3 + 7}{2}) + 2 πn

cos (x) = - \frac{3 + 7}{2} :

No Solution

Combine all the solutions

x = arccos (\frac{- 3 + 7}{2}) + 2 πn, x = - arccos (\frac{- 3 + 7}{2}) + 2 πn

Show solutions in decimal form

x = 1.74886 \dots + 2 πn, x = - 1.74886 \dots + 2 πn

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

22 = 18 + 8 cos (\frac{x + 9}{12} π)

sin (2 x) tan (x) = sin (x)

3 sin^{3} (x) = 0

tan (x) (tan (x) - 3) + 2 = 0

What is the general solution for 2cos^2(x)+6cos(x)=-1 ?
The general solution for 2cos^2(x)+6cos(x)=-1 is x=1.74886…+2pin,x=-1.74886…+2pin