`sqrt(113+ x+196)=22`

Options

A. 160
B. 122
C. 158
D. 150

Explanation

To solve the equation \( \sqrt{113 + x + 196} = 22 \), we will follow these steps:

### Step 1: Remove the square root
To eliminate the square root, we will square both sides of the equation.

\[ \left(\sqrt{113 + x + 196}\right)^2 = 22^2 \]

This simplifies to:

\[ 113 + x + 196 = 484 \]

### Step 2: Combine like terms
Next, we will combine the constants on the left side of the equation.

\[ (113 + 196) + x = 484 \]

Calculating \( 113 + 196 \):

\[ 309 + x = 484 \]

### Step 3: Isolate \( x \)
To find the value of \( x \), we need to isolate it by subtracting 309 from both sides of the equation.

\[ x = 484 - 309 \]

### Step 4: Calculate the value of \( x \)
Now, we will perform the subtraction.

\[ x = 175 \]

Thus, the value of \( x \) is \( 175 \).

### Final Answer:
\[ x = 175 \]

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