91Ó°ÊÓ

When solving an equation for a specific variable, the first step is often to isolate that variable. This means getting the variable alone on one side of the equation. For example, in the formula \( F = \frac{kA}{v^2} \), our goal is to isolate \(v\).
To do this, we might need to perform a series of operations like multiplication, division, addition, or subtraction. Here, multiplying both sides by \(v^2\) helps move the \(v^2\) term from the denominator to the numerator, making it easier to isolate:
\[ Fv^2 = kA \]
By doing this, we have successfully isolated the variable \(v^2\). Always remember, isolating the variable is a crucial step before solving it. It lays the groundwork for simplifying and solving the equation step-by-step.

Once the variable is isolated, the next task is to solve for it. Let's continue with our isolated term:
\[ Fv^2 = kA \]
We need to solve for \(v\). First, we rearrange the equation to make \(v^2\) the subject. This is done by dividing both sides by \(F\):
\[ v^2 = \frac{kA}{F} \]
This division helps us to further isolate \(v^2\), bringing us closer to solving for \(v\). The goal in solving for a variable is to have it by itself on one side, with no additional coefficients or terms. By methodically performing inverse operations like multiplication/division or addition/subtraction, we can solve for the target variable.
Always remember to maintain the equality of the equation by performing the same operations on both sides.

Our final step is to solve for \(v\) by taking the square root of both sides of the equation. We currently have:
\[ v^2 = \frac{kA}{F} \]
Taking the square root of both sides helps to eliminate the square on the left side:
\[ v = \sqrt{\frac{kA}{F}} \]
This gives us the solution for \(v\). It's important to note that when you take the square root of both sides, you consider both the positive and negative roots. However, depending on the context, you might select the positive root (e.g., if dealing with physical measurements).
By taking the square root of both sides, you effectively solve for the variable in its simplest form. Ensure you perform this step carefully to avoid errors.