https://file.aiquickdraw.com/mathbot/file/172414796358930puybuo.jpg

The image you uploaded contains a mathematical equation that has been worked on. Let's go through the steps shown in the image to solve the equation:

1. The equation starts with:
   \[
   2^{x+2} = \sqrt{2}
   \]

2. The square root of 2 can be rewritten as a power of 2:
   \[
   \sqrt{2} = 2^{\frac{1}{2}}
   \]
   So, the equation becomes:
   \[
   2^{x+2} = 2^{\frac{1}{2}}
   \]

3. Since the bases on both sides of the equation are the same (both are base 2), we can set the exponents equal to each other:
   \[
   x + 2 = \frac{1}{2}
   \]

4. To solve for \( x \), subtract 2 from both sides:
   \[
   x = \frac{1}{2} - 2
   \]

5. Simplify the right-hand side:
   \[
   x = \frac{1}{2} - \frac{4}{2} = \frac{-3}{2}
   \]
   Thus, \( x = -\frac{3}{2} \).

So, the solution to the equation is \( x = -\frac{3}{2} \).

Would you like more details on any of the steps? Here are some related questions:

1. How can you convert roots into exponents?
2. What is the general approach to solving exponential equations with the same base?
3. How do you simplify expressions involving fractions?
4. What is the significance of logarithms in solving exponential equations?
5. Can this problem be solved using logarithms?

**Tip:** When dealing with equations involving exponents, always look for ways to express all terms with the same base to simplify the solving process.

Learn how to solve the exponential equation 2^(x+2) = sqrt(2) with a detailed step-by-step solution. This problem covers solving equations with exponents and understanding the relationship between exponents and roots. Suitable for students in Grades 9-12.

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