√7-√x+1=2

To solve the equation \( \sqrt{7} - \sqrt{x} + 1 = 2 \), let's start by isolating the square root:

1. Subtract 1 from both sides: \[ \sqrt{7} - \sqrt{x} = 1 \]

2. Next, isolate \( \sqrt{x} \) by subtracting \( \sqrt{7} \) from both sides: \[ -\sqrt{x} = 1 - \sqrt{7} \]

3. Multiply both sides by -1: \[ \sqrt{x} = \sqrt{7} - 1 \]

4. Now, square both sides to eliminate the square root: \[ x = (\sqrt{7} - 1)^2 \]

5. Expand the right-hand side: \[ x = (\sqrt{7})^2 - 2 \cdot \sqrt{7} \cdot 1 + 1^2 \] \[ x = 7 - 2\sqrt{7} + 1 \] \[ x = 8 - 2\sqrt{7} \]

Thus, the solution to the equation \( \sqrt{7} - \sqrt{x} + 1 = 2 \) is: \[ x = 8 - 2\sqrt{7} \]