We start with the equation:

\[
\sqrt{x} - 1 = 5 - \sqrt{x} + 4
\]

First, simplify the right-hand side:

\[
\sqrt{x} - 1 = 9 - \sqrt{x}
\]

Now, let's combine like terms by adding \(\sqrt{x}\) to both sides:

\[
\sqrt{x} + \sqrt{x} - 1 = 9
\]

This simplifies to:

\[
2\sqrt{x} - 1 = 9
\]

Next, add 1 to both sides:

\[
2\sqrt{x} = 10
\]

Now, divide both sides by 2:

\[
\sqrt{x} = 5
\]

Finally, square both sides to eliminate the square root:

\[
x = 25
\]

Let's verify by substituting \(x = 25\) back into the original equation:

\[
\sqrt{25} - 1 = 5 - \sqrt{25} + 4
\]

This simplifies to:

\[
5 - 1 = 5 - 5 + 4
\]

\[
4 = 4
\]

Thus, the solution is correct. The value of \(x\) is:

\[
\boxed{25}
\]

Would you like further details or have any questions? 

Here are 5 related questions for practice:

1. Solve \(\sqrt{x} - 2 = 6 - \sqrt{x}\).
2. Solve \(3\sqrt{x} + 4 = 10\).
3. Find \(x\) if \(2\sqrt{x} + 3 = \sqrt{x + 9}\).
4. Solve \(\sqrt{2x + 1} - \sqrt{x} = 3\).
5. Find the value of \(x\) in \(\sqrt{3x} + 5 = 11\).

**Tip**: Always check your solutions by substituting them back into the original equation, especially when dealing with square roots.

Discover how to solve the square root equation √x - 1 = 5 - √x + 4 with a clear step-by-step solution. This problem focuses on algebraic manipulation involving square roots, suitable for students in Grades 9-10.

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