Find the value of x, if
`10000x = (9982) ^(2) - (18) ^(2)`

Answer

To find the value of \( x \) in the equation \( 10000x = (9982)^2 - (18)^2 \), we can follow these steps:

### Step 1: Recognize the Difference of Squares
We know that the expression \( a^2 - b^2 \) can be factored using the identity:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, let \( a = 9982 \) and \( b = 18 \).

### Step 2: Apply the Identity
Using the difference of squares identity:
\[ (9982)^2 - (18)^2 = (9982 - 18)(9982 + 18) \]

### Step 3: Calculate \( 9982 - 18 \) and \( 9982 + 18 \)
Now, we calculate the two terms:
\[ 9982 - 18 = 9964 \]
\[ 9982 + 18 = 10000 \]

### Step 4: Substitute Back into the Equation
Now substitute these values back into the equation:
\[ 10000x = (9964)(10000) \]

### Step 5: Simplify the Equation
Now, we can simplify the equation:
\[ 10000x = 9964 \times 10000 \]
Dividing both sides by \( 10000 \):
\[ x = 9964 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{9964} \]