The problem is asking for the value of \( x \) such that the distance between the points \( (x, 8) \) and \( (3, 3) \) is zero.

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Given that the distance \( d = 0 \), this implies the two points must be the same.

Let's set up the equation using the points \( (x, 8) \) and \( (3, 3) \):

\[
\sqrt{(3 - x)^2 + (3 - 8)^2} = 0
\]

Since the square root of any non-negative number is zero only when the number itself is zero, we can set the expression inside the square root to zero:

\[
(3 - x)^2 + (3 - 8)^2 = 0
\]

Simplifying this:

\[
(3 - x)^2 + (-5)^2 = 0
\]

\[
(3 - x)^2 + 25 = 0
\]

Now, for this equation to hold, \( (3 - x)^2 \) must equal \(-25\). However, the square of any real number cannot be negative, which implies there is no real solution.

Therefore, for the distance to be zero, the only way the points can coincide is if the points are identical, meaning \( (x, 8) \) must be the same as \( (3, 3) \). This requires:

\[
x = 3 \quad \text{and} \quad 8 = 3
\]

But since \( 8 \neq 3 \), this is impossible. Thus, under normal conditions, the equation cannot be satisfied by any real value of \( x \). If the condition \( d = 0 \) is strictly required, then there is **no solution**.

Would you like more details, or do you have any other questions?

Here are some related questions to explore:

1. What is the distance formula between two points in 3D space?
2. How do you solve equations involving absolute values?
3. What are the conditions for two points to be the same?
4. Can you solve equations involving complex numbers?
5. How does the concept of distance apply in higher dimensions?

**Tip:** Always double-check whether the problem allows for non-real solutions, as that can change the outcome.

Explore how to solve the problem involving the distance between points (x, 8) and (3, 3). Understand the application of the distance formula in Cartesian coordinates. Suitable for advanced high school students.

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