https://file.aiquickdraw.com/mathbot/file/1726432573886jett2cr3.jpg

The image shows the equation:

\[
X = (X - 1)^2 = m = 64
\]

This equation involves multiple equalities, where \( X \), \( m \), and \( 64 \) are related through the expression \( (X - 1)^2 \).

### Let's solve this step by step:

1. **Start with the equation \( (X - 1)^2 = 64 \):**
   \[
   (X - 1)^2 = 64
   \]
   Take the square root of both sides:
   \[
   X - 1 = \pm 8
   \]
   This gives two solutions:
   \[
   X - 1 = 8 \quad \text{or} \quad X - 1 = -8
   \]
   Solving for \( X \):
   \[
   X = 9 \quad \text{or} \quad X = -7
   \]

2. **Check the equality with \( X = 9 \) and \( X = -7 \):**
   Since the equation says \( X = (X - 1)^2 = m = 64 \), we check both solutions:

   - For \( X = 9 \), we have:
     \[
     (9 - 1)^2 = 8^2 = 64
     \]
     This satisfies the equation.

   - For \( X = -7 \), we have:
     \[
     (-7 - 1)^2 = (-8)^2 = 64
     \]
     This also satisfies the equation.

Thus, both \( X = 9 \) and \( X = -7 \) are valid solutions.

---

Do you have any questions or would you like more details on any part of the process? Here are some follow-up questions you might consider:

1. Why are there two solutions when we solve \( (X - 1)^2 = 64 \)?
2. What is the significance of the square root in equations like these?
3. How can this equation be represented graphically?
4. Could the problem be solved using a different method, like factoring?
5. How does the concept of absolute value play into this type of equation?

**Tip:** When solving equations involving squares, always check for both the positive and negative roots!

Solve the equation X = (X - 1)^2 = m = 64.

Learn how to solve the quadratic equation X = (X - 1)^2 = m = 64 with a detailed step-by-step solution. This equation highlights key algebraic principles such as the square root property, and offers solutions for X = 9 and X = -7. Suitable for students in Grades 9-10.

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