Solve $2{\cos }^2(w)-3\cos (w)+1=0$ for all solutions.
$$w=◻+2k\pi \text{; Select an answer (0) }$$

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Step 1 ：First, we need to solve the quadratic equation $2{\cos }^2(w)-3\cos (w)+1=0$. We can do this by using the quadratic formula, which gives us the roots of the equation.

Step 2 ：The roots of the quadratic equation are the possible values for $\cos (w)$. We find that the roots are 1 and 0.5.

Step 3 ：Next, we use the arccosine function to find the corresponding values of $w$. The arccosine of 1 is 0, and the arccosine of 0.5 is $\frac{\pi }{3}$ (or approximately 1.047).

Step 4 ：However, these are not the only solutions. Since the cosine function has a period of $2\pi$, we can add $2k\pi$ to these solutions to get the general solutions, where $k$ is an integer.

Step 5 ：The general solutions are $w=\boxed{{\displaystyle 0+2k\pi }}$ and $w=\boxed{{\displaystyle \frac{\pi }{3}+2k\pi }}$, where $k$ is an integer.