`(23.1)^(2)+(48.6)^(2)-(39.8)^(2)=?+1147.69`

Options

A. `(13.6)^(2)`
B. `sqrt(12.8)`
C. 163.84
D. 12.8

Explanation

To solve the equation \( (23.1)^{2} + (48.6)^{2} - (39.8)^{2} = ? + 1147.69 \), we will follow these steps:

### Step 1: Calculate \( (23.1)^{2} \)
\[ (23.1)^{2} = 23.1 \times 23.1 = 533.61 \]

### Step 2: Calculate \( (48.6)^{2} \)
\[ (48.6)^{2} = 48.6 \times 48.6 = 2361.96 \]

### Step 3: Calculate \( (39.8)^{2} \)
\[ (39.8)^{2} = 39.8 \times 39.8 = 1584.04 \]

### Step 4: Substitute the values into the equation
Now substitute the calculated squares back into the equation:
\[ 533.61 + 2361.96 - 1584.04 = ? + 1147.69 \]

### Step 5: Simplify the left side
First, we add \( 533.61 \) and \( 2361.96 \):
\[ 533.61 + 2361.96 = 2895.57 \]
Now subtract \( 1584.04 \):
\[ 2895.57 - 1584.04 = 1311.53 \]

### Step 6: Set up the equation to solve for \( ? \)
Now we have:
\[ 1311.53 = ? + 1147.69 \]

### Step 7: Isolate \( ? \)
To find \( ? \), subtract \( 1147.69 \) from both sides:
\[ ? = 1311.53 - 1147.69 \]

### Step 8: Calculate the final value of \( ? \)
\[ ? = 163.84 \]

### Final Answer
Thus, the value of \( ? \) is \( 163.84 \).

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