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The equation provided is:

\[
(x - 2)^2 + 4 = 5
\]

To solve this quadratic equation for \(x\), let's proceed step by step:

### Step 1: Subtract 4 from both sides
\[
(x - 2)^2 + 4 - 4 = 5 - 4
\]
\[
(x - 2)^2 = 1
\]

### Step 2: Take the square root of both sides
\[
x - 2 = \pm \sqrt{1}
\]
\[
x - 2 = \pm 1
\]

### Step 3: Solve for \(x\)
Now, solve for \(x\) for both the positive and negative cases:

- For \(x - 2 = 1\):
\[
x = 1 + 2 = 3
\]

- For \(x - 2 = -1\):
\[
x = -1 + 2 = 1
\]

### Final Answer:
The solutions are \(x = 3\) and \(x = 1\).

Would you like more details, or do you have any questions?

Here are some related questions:
1. How would the solution change if the constant term on the right side was different?
2. What if the equation was \((x - a)^2 + b = c\) in general form?
3. How can you verify that the solutions are correct?
4. What if the discriminant was negative? How would that affect the solutions?
5. How do you solve quadratic equations if the square is expanded (e.g., \(ax^2 + bx + c = 0\))?

**Tip:** Always isolate the squared term first to make solving quadratic equations easier.

Solve the following quadratic equation for all values of x in simplest form: (x - 2)^2 + 4 = 5.

Learn how to solve the quadratic equation (x - 2)^2 + 4 = 5 using the square root property. This problem demonstrates step-by-step solutions involving algebraic manipulation, suitable for students in Grades 7-9.

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