The image provided involves the equation $K = \frac{1}{2} mv^2$, which has been manipulated step by step. Let's analyze and solve for $v$, as appears to be the goal.

Steps:

1. The original equation is: $K = \frac{1}{2}mv^2$
2. Multiply both sides by 2 to eliminate the fraction: $K \cdot 2 = mv^2$
3. The current equation is: $2K = mv^2$
4. Divide both sides by $m$ to isolate $v^2$: $\frac{2K}{m} = v^2$
5. Take the square root of both sides to solve for $v$: $v = \sqrt{\frac{2K}{m}}$

This simplifies the equation to find $v$ in terms of $K$ and $m$.

Explanation:

This sequence uses standard algebraic techniques: multiplying to clear fractions, isolating the variable, and using the square root to undo the square.

Do you have any questions or need further clarification?
Here are five related questions you might consider:

1. Can you explain why we take the square root at the last step?
2. How do physical principles relate to this equation?
3. Could $K$, $m$, or $v$ ever have negative values in practical physics problems?
4. How could this formula be applied to real-world scenarios, such as kinetic energy?
5. What are some alternative methods for solving equations like this one?

Tip: Always check the dimensions (units) in physics-based equations to ensure correctness!