https://file.aiquickdraw.com/mathbot/file/1727240185749k4gujoo2.jpg

Let's walk through the process of completing the square to solve the equation \(x^2 - 4x = 1\) as shown in the image.

1. The given equation is:

   \[
   x^2 - 4x = 1
   \]

2. To complete the square, we focus on the quadratic and linear terms on the left-hand side (\(x^2 - 4x\)).

3. Take the coefficient of \(x\), which is \(-4\), divide it by 2, and then square the result:

   \[
   \left(\frac{-4}{2}\right)^2 = 4
   \]

4. Add this squared value to both sides of the equation to keep it balanced:

   \[
   x^2 - 4x + 4 = 1 + 4
   \]

5. Now, the left-hand side becomes a perfect square:

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

So, the correct steps are:
- Add 4 to both sides, turning the equation into \( (x - 2)^2 = 5 \).

Thus, the correct choice is **Option C**.

Would you like a detailed breakdown of this process? Here are some related questions you can explore:

1. What are the general steps to complete the square for any quadratic equation?
2. How do you solve \( (x - 2)^2 = 5 \) from the final step?
3. Can every quadratic equation be solved by completing the square?
4. How is completing the square related to the quadratic formula?
5. What practical applications use the method of completing the square?

**Tip**: Completing the square is especially useful in converting quadratic equations into vertex form, which helps in graphing and analyzing their properties.

Solve the quadratic equation by completing the square: x^2 - 4x = 1.

Learn how to solve the quadratic equation x^2 - 4x = 1 using the method of completing the square. This step-by-step solution explains key algebraic concepts, including quadratic equations, completing the square, and properties of quadratics. Suitable for students in Grades 8-10.

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