https://file.aiquickdraw.com/mathbot/file/1725672494571foee9z8p.jpg

It seems the text extraction wasn't clear. However, visually analyzing the image, the equation appears to be:

\[
\sqrt{6x + 5} = \sqrt{2x + 10}
\]

Let me now solve this equation.

### Step-by-Step Solution:

1. **Square both sides** to eliminate the square roots:
   \[
   (\sqrt{6x + 5})^2 = (\sqrt{2x + 10})^2
   \]
   This simplifies to:
   \[
   6x + 5 = 2x + 10
   \]

2. **Isolate** the variable by subtracting \(2x\) from both sides:
   \[
   6x - 2x + 5 = 10
   \]
   \[
   4x + 5 = 10
   \]

3. **Solve for** \(x\):
   Subtract 5 from both sides:
   \[
   4x = 5
   \]
   Divide by 4:
   \[
   x = \frac{5}{4} = 1.25
   \]

### Conclusion:
The solution to the equation is \(x = 1.25\).

Would you like further details on any of these steps or have additional questions?

Here are some related questions:
1. How can we verify if \(x = 1.25\) satisfies the original equation?
2. What happens if the square roots were unequal (e.g., \(\sqrt{6x + 5} \neq \sqrt{2x + 10}\))?
3. How would the equation change if one side involved a cube root instead of a square root?
4. Can this technique be applied to equations involving more complicated radical expressions?
5. What other methods, besides squaring, could we use to solve radical equations?

**Tip:** When dealing with square roots in an equation, always check your solution to ensure it doesn't introduce extraneous solutions.

Solve the equation: √(6x + 5) = √(2x + 10).

Learn how to solve the radical equation √(6x + 5) = √(2x + 10) with a detailed step-by-step solution. This problem involves algebraic concepts such as radical equations and squaring both sides to eliminate square roots. Suitable for students in Grades 9-10.

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