`?^(2)+214.09-24.06xx5.14=319.19`

Options

A. 7
B. 13
C. 11
D. 15

Explanation

To solve the equation \( ?^2 + 214.09 - 24.06 \times 5.14 = 319.19 \), we will follow these steps:

### Step 1: Approximate the values
We will round the decimal numbers to the nearest integers for easier calculations:
- \( 214.09 \) rounds to \( 214 \)
- \( 24.06 \) rounds to \( 24 \)
- \( 5.14 \) rounds to \( 5 \)
- \( 319.19 \) rounds to \( 319 \)

### Step 2: Rewrite the equation with approximations
Now, we can rewrite the equation using the approximated values:
\[ ?^2 + 214 - 24 \times 5 = 319 \]

### Step 3: Calculate \( 24 \times 5 \)
Next, we calculate \( 24 \times 5 \):
\[ 24 \times 5 = 120 \]

### Step 4: Substitute back into the equation
Now substitute this back into the equation:
\[ ?^2 + 214 - 120 = 319 \]

### Step 5: Simplify the equation
Simplifying the left side gives:
\[ ?^2 + 94 = 319 \]

### Step 6: Isolate \( ?^2 \)
Now, isolate \( ?^2 \) by subtracting \( 94 \) from both sides:
\[ ?^2 = 319 - 94 \]

### Step 7: Calculate \( 319 - 94 \)
Now, perform the subtraction:
\[ 319 - 94 = 225 \]

### Step 8: Solve for \( ? \)
Now we take the square root of both sides to find \( ? \):
\[ ? = \sqrt{225} \]

### Step 9: Calculate the square root
Calculating the square root gives:
\[ ? = 15 \]

### Conclusion
Thus, the value of \( ? \) is \( 15 \).

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