What is the general solution for cos^2(x)+cos(x)+1=0 ?

The general solution for cos^2(x)+cos(x)+1=0 is No Solution for x\in\mathbb{R}

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cos^2(x)+cos(x)+1=0

cos^{2} (x) + cos (x) + 1 = 0

No Solution for x \in R

Solution steps

cos^{2} (x) + cos (x) + 1 = 0

Solve by substitution

cos (x) = - \frac{1}{2} + i \frac{3}{2}, cos (x) = - \frac{1}{2} - i \frac{3}{2}

cos (x) = - \frac{1}{2} + i \frac{3}{2} :

No Solution

cos (x) = - \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

No Solution for x \in R

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

3 tan^{2} (x) - 3 tan (x) = 0

- 4 sec^{2} (x) + 19 = - 4 tan (x)

4 sin (x) + 6 = 6

tan (2 x - \frac{π}{6}) = \frac{- 1}{3}

What is the general solution for cos^2(x)+cos(x)+1=0 ?
The general solution for cos^2(x)+cos(x)+1=0 is No Solution for x\in\mathbb{R}