If `sqrt(x)-sqrt(12)=sqrt(4)-sqrt(x)` , then find `x` .

Answer

To solve the equation \( \sqrt{x} - \sqrt{12} = \sqrt{4} - \sqrt{x} \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ \sqrt{x} - \sqrt{12} = \sqrt{4} - \sqrt{x} \]

### Step 2: Move all terms involving \( \sqrt{x} \) to one side
Add \( \sqrt{x} \) to both sides:
\[ \sqrt{x} + \sqrt{x} - \sqrt{12} = \sqrt{4} \]
This simplifies to:
\[ 2\sqrt{x} - \sqrt{12} = \sqrt{4} \]

### Step 3: Substitute the values of square roots
We know that \( \sqrt{12} = 2\sqrt{3} \) and \( \sqrt{4} = 2 \). Substitute these values into the equation:
\[ 2\sqrt{x} - 2\sqrt{3} = 2 \]

### Step 4: Isolate the term with \( \sqrt{x} \)
Add \( 2\sqrt{3} \) to both sides:
\[ 2\sqrt{x} = 2 + 2\sqrt{3} \]

### Step 5: Divide both sides by 2
\[ \sqrt{x} = 1 + \sqrt{3} \]

### Step 6: Square both sides to solve for \( x \)
Now, square both sides to eliminate the square root:
\[ x = (1 + \sqrt{3})^2 \]

### Step 7: Expand the squared term
Using the formula \( (a + b)^2 = a^2 + 2ab + b^2 \):
\[ x = 1^2 + 2 \cdot 1 \cdot \sqrt{3} + (\sqrt{3})^2 \]
This simplifies to:
\[ x = 1 + 2\sqrt{3} + 3 \]
\[ x = 4 + 2\sqrt{3} \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{4 + 2\sqrt{3}} \]

---