choose a form: (x+?)^2 = ? or (x-?)^2 = ? then give me a solution after you have pick one form

Let's choose the form \((x - ?)^{2} = ?\).

I'll go with the form \((x - 3)^{2} = 25\). Here's the solution:

### Step 1: Expand the equation
We have:
\[
(x - 3)^{2} = 25
\]
To solve for \(x\), we first take the square root of both sides:
\[
x - 3 = \pm \sqrt{25}
\]
\[
x - 3 = \pm 5
\]

### Step 2: Solve for \(x\)
Now, solve for \(x\) in both cases:
1. \(x - 3 = 5\), so \(x = 5 + 3 = 8\)
2. \(x - 3 = -5\), so \(x = -5 + 3 = -2\)

### Final answer:
\[
x = 8 \quad \text{or} \quad x = -2
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you solve \((x - 5)^2 = 16\)?
2. What if the equation was \((x + 2)^2 = 49\)?
3. Can you solve \((x - 4)^2 = 9\)?
4. How would you approach \((x - 6)^2 = 0\)?
5. How do you solve \((x - 7)^2 = 36\)?

**Tip:** When solving equations like \((x - a)^2 = b\), always remember to consider both the positive and negative square roots.

Explore how to solve the quadratic equation (x - 3)^2 = 25 using algebraic methods. This detailed solution covers the expansion, square root property, and solving for x. Perfect for students in Grades 7-9 learning about quadratic equations.

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