To find the number that should be added to both sides to make a perfect square, we need to complete the square for the expression given:

$0 = x^2 - 4x + 7$

1. Isolate the quadratic and linear terms: Focus on $x^2 - 4x$.

2. Find the number to complete the square:

   • Take half of the coefficient of $x$, which is $-4$, so $\frac{-4}{2} = -2$.
   • Square this result: $(-2)^2 = 4$.

3. Add and subtract this square term: To make a perfect square, we would add $4$ to both sides. The expression becomes: $0 = (x^2 - 4x + 4) + 7 - 4$ Simplifying, we get: $0 = (x - 2)^2 + 3$

So, the correct answer is 4.

Would you like a deeper explanation of the completing the square method, or do you have any other questions?

Here are five related questions:

1. How do you complete the square for other quadratic equations?
2. What is the purpose of completing the square in algebra?
3. How does completing the square relate to solving quadratic equations?
4. Can completing the square help in finding the vertex form of a quadratic equation?
5. How is completing the square used in calculus?

Tip: Completing the square is useful for transforming quadratic equations into vertex form, making it easier to analyze the function's properties like vertex and axis of symmetry.