Please solve. Take into account that the first variable is y=4sqrt(x-2)

Let's first break down the given equation \( y = 4\sqrt{x-2} \). The task is to analyze it and solve for a particular variable, but since no other equation is provided, I will assume you want to solve for \( x \) in terms of \( y \). 

### Given:
\[
y = 4\sqrt{x-2}
\]

### To solve for \( x \):
1. First, divide both sides of the equation by 4:
   \[
   \frac{y}{4} = \sqrt{x-2}
   \]

2. Square both sides to eliminate the square root:
   \[
   \left( \frac{y}{4} \right)^2 = x - 2
   \]

3. Simplify:
   \[
   \frac{y^2}{16} = x - 2
   \]

4. Finally, solve for \( x \):
   \[
   x = \frac{y^2}{16} + 2
   \]

### Final solution:
\[
x = \frac{y^2}{16} + 2
\]

Would you like more details or clarifications on any step?

### Related Questions:
1. How do we handle square roots and squaring in general?
2. What are the restrictions on \( x \) based on the square root function?
3. How do we graph this equation \( y = 4\sqrt{x-2} \)?
4. What if \( y \) or \( x \) has real-world applications, such as in physics?
5. Can we generalize this formula for different constants other than 4?

### Tip: 
When dealing with square roots, always check if the expression under the square root is non-negative, as the square root of a negative number is undefined in the real number system.

Please solve. Take into account that the first variable is y=4sqrt(x-2).

Learn how to solve the radical equation y = 4√(x - 2) and find x in terms of y. This step-by-step guide covers algebraic concepts such as square roots, inverse operations, and radical equations. Ideal for students in Grades 9-10.

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