Please solve this equation

Question

I think I'm missing something here. Please include steps solving this equation to $x$.

$$0=\cos^2{x}+\cos{x}-\sin^2{x}$$

Answer 1

\begin{align} \cos^2x+\cos x-\sin^2x&=0\\ \cos^2x+\cos x-(1-\cos^2x)&=0\\ 2\cos^2x+\cos x-1&=0\\ (2\cos x-1)(\cos x+1)&=0 \end{align}

Answer 2

$$\cos x=-(\cos^2x-\sin^2x)\iff\cos2x=\cos(\pi+x)$$

$$2x=2n\pi\pm(\pi+x)$$ where $n$ is any integer