If `19x^2 = 100^2 - 90^2`, then find the value of x
A. 10
B. 9
C. 11
D. 12

Options

A. C
B. A
C. D
D. B

Answer

To solve the equation \( 19x^2 = 100^2 - 90^2 \), we will follow these steps:

### Step 1: Simplify the Right Side Using the Difference of Squares
We know that \( a^2 - b^2 = (a - b)(a + b) \). Here, let \( a = 100 \) and \( b = 90 \).

\[ 100^2 - 90^2 = (100 - 90)(100 + 90) \]

### Step 2: Calculate the Values
Now, calculate \( 100 - 90 \) and \( 100 + 90 \):

\[ 100 - 90 = 10 \]
\[ 100 + 90 = 190 \]

### Step 3: Substitute Back into the Equation
Now substitute these values back into the equation:

\[ 100^2 - 90^2 = 10 \times 190 = 1900 \]

So, we have:

\[ 19x^2 = 1900 \]

### Step 4: Isolate \( x^2 \)
To find \( x^2 \), divide both sides by 19:

\[ x^2 = \frac{1900}{19} \]

### Step 5: Calculate \( \frac{1900}{19} \)
Now perform the division:

\[ \frac{1900}{19} = 100 \]

### Step 6: Take the Square Root
Now, take the square root of both sides to find \( x \):

\[ x = \sqrt{100} = 10 \]

### Conclusion
Thus, the value of \( x \) is \( 10 \).

### Final Answer
The correct option is **A. 10**.

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