To solve the equation \(\sqrt{x} - 2\sqrt{x} + 7 = 11\), we first simplify the left side.
The equation can be simplified as follows:
\[ \sqrt{x} - 2\sqrt{x} + 7 = 11 \]
Combining the terms involving \(\sqrt{x}\):
\[ -\sqrt{x} + 7 = 11 \]
Next, we isolate \(-\sqrt{x}\):
\[ -\sqrt{x} = 11 - 7 \]
\[ -\sqrt{x} = 4 \]
Now, multiply both sides by -1:
\[ \sqrt{x} = -4 \]
However, a square root cannot be negative, which indicates that there are no real solutions to this equation.
Thus, the conclusion is that the equation has no real solutions.