What is the first step in solving a formula like \( g w^{2}=2 r \) for \( w ? \)

To isolate \( w \), the first step is to divide both sides of the equation by \( g \) to get rid of the coefficient. This alters the equation to \( w^{2} = \frac{2 r}{g} \). Simplifying the equation at this point sets you on the right path to solving for \( w \) in the next steps! Once you have \( w^{2} = \frac{2 r}{g} \), the next logical step is to take the square root of both sides. When you do this, don't forget about the positive and negative roots! So, you will get \( w = \pm \sqrt{\frac{2 r}{g}} \). And voila, you've found \( w \)!