https://file.aiquickdraw.com/mathbot/file/1725672431692imrrpehg.jpg

The equation in the image appears to be:

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

Let's solve for \( x \).

### Step-by-step solution:

1. **Square both sides** to eliminate the square roots:
   \[
   (3\sqrt{6x + 5})^2 = (\sqrt{2x + 10})^2
   \]
   Simplifying:
   \[
   9(6x + 5) = 2x + 10
   \]
   This expands to:
   \[
   54x + 45 = 2x + 10
   \]

2. **Move all terms involving \(x\)** to one side:
   \[
   54x - 2x = 10 - 45
   \]
   Simplifying:
   \[
   52x = -35
   \]

3. **Solve for \(x\)**:
   \[
   x = \frac{-35}{52}
   \]

   Simplifying the fraction:
   \[
   x = \frac{-35}{52} = \frac{-5}{8}
   \]

Thus, the solution is \( x = -\frac{5}{8} \).

Would you like more details on the solution steps, or do you have any further questions?

### Related Questions:
1. What happens if both sides of the equation are squared incorrectly?
2. How do you verify if \( x = -\frac{5}{8} \) satisfies the original equation?
3. What if the equation had cube roots instead of square roots?
4. How would the solution change if the equation had a coefficient in front of the second square root?
5. Can this method be applied to equations with multiple square roots?

### Tip:
Always check your solutions by substituting back into the original equation to ensure no extraneous solutions arise from squaring both sides.

Learn how to solve the square root equation 3√(6x + 5) = √(2x + 10) with a detailed step-by-step explanation. The solution involves squaring both sides and solving for x, covering key algebraic concepts like square roots and linear equations. Suitable for students in Grades 10-12.

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