No, there are no other real solutions for \( x \).

After solving the equation \( 2x + \sqrt{x + 6} = 9 \), we found two potential solutions: \( x = 6.25 \) and \( x = 3 \). Upon checking these solutions in the original equation, only \( x = 3 \) satisfies the equation, while \( x = 6.25 \) does not. Therefore, the only real solution is \( x = 3 \).

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**Tip:** Be cautious when solving equations involving square roots, as the squaring process can introduce extraneous solutions that need to be checked against the original equation.

Explore how to find real solutions for the equation 2x + sqrt(x + 6) = 9. Understand the process of solving equations involving square roots, including checking solutions for validity. Detailed solution analysis provided.

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