The equation you provided is:

\[
3 \sqrt{x} - 1 = \sqrt{x} + 207
\]

Let's solve this step by step.

### Step 1: Isolate the square root term
First, we'll isolate one of the square root terms on one side of the equation. We'll subtract \(\sqrt{x}\) from both sides:

\[
3 \sqrt{x} - \sqrt{x} - 1 = 207
\]

This simplifies to:

\[
2 \sqrt{x} - 1 = 207
\]

### Step 2: Isolate \(\sqrt{x}\)
Next, we'll add 1 to both sides to isolate \(2 \sqrt{x}\):

\[
2 \sqrt{x} = 208
\]

### Step 3: Solve for \(\sqrt{x}\)
Now, divide both sides by 2:

\[
\sqrt{x} = 104
\]

### Step 4: Square both sides to eliminate the square root
Square both sides to solve for \(x\):

\[
x = 104^2
\]

\[
x = 10816
\]

So, the solution is:

\[
x = 10816
\]

Would you like more details or have any questions about this solution?

### Relative Questions:
1. How do you solve equations involving square roots and other radicals?
2. What happens if the square root term appears on both sides of the equation?
3. Can you explain how to check the solution in a square root equation?
4. What are some common mistakes to avoid when solving radical equations?
5. How would the process change if there were higher-order roots, like cube roots?

**Tip:** Always check your solutions when dealing with square roots or other radicals to ensure no extraneous solutions are introduced.

Learn how to solve the equation 3√x - 1 = √x + 207 step-by-step with detailed explanations and calculations. This problem involves equations with square roots and isolating variables, suitable for advanced high school students.

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