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

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

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

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

No Solution for x \in R

Solution steps

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

Solve by substitution

cos (x) = - \frac{1}{4} + i \frac{7}{4}, cos (x) = - \frac{1}{4} - i \frac{7}{4}

cos (x) = - \frac{1}{4} + i \frac{7}{4} :

No Solution

cos (x) = - \frac{1}{4} - i \frac{7}{4} :

No Solution

Combine all the solutions

No Solution for x \in R

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

- 2 + 3 csc (x) = 5

2 sin (2 x) = sin (4 x), 0 \leq x \leq π

9 sin (x) - 2 = 4 sin^{2} (x)

- a c_{1} sin (a x) + a c_{2} cos (a x) = 0

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