https://file.aiquickdraw.com/mathbot/file/17256669886048iltekpz.jpg

The equation provided in the image is:

\[
(2x - 5)^2 + 5 = 3
\]

Let's solve this step by step:

### Step 1: Isolate the squared term
First, subtract 5 from both sides of the equation to simplify:

\[
(2x - 5)^2 + 5 - 5 = 3 - 5
\]
\[
(2x - 5)^2 = -2
\]

### Step 2: Analyze the squared term
Since the square of a real number is always non-negative, and the right side of the equation is \(-2\), which is negative, **there are no real solutions** for this equation.

### Conclusion:
There are no real values of \(x\) that satisfy this equation.

Would you like more details or have any questions?

Here are some related questions for practice:
1. How would the solution change if the right-hand side were positive?
2. What are the properties of quadratic equations that lead to no real solutions?
3. Can we find complex solutions for this equation? If so, how?
4. What would happen if the constant 5 on the left-hand side were negative instead?
5. How can we graphically represent this equation?

**Tip:** When solving quadratic equations, always check if the right side is positive before taking square roots!

Learn how to solve the quadratic equation (2x - 5)^2 + 5 = 3 and understand why there are no real solutions. This problem covers important algebraic concepts and the non-negative property of squares. Suitable for students in Grades 9-11.

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