What number should be added to the expression x² + 4x to make it a perfect square?

Completing the Square

To find the number that should be added to the expression x² + 4x to make it a perfect square, we can follow these steps:

1. Start with the given expression: x² + 4x.
2. Identify the coefficient of the linear term (4x). In this case, the coefficient is 4.
3. Take half of the coefficient of x (which is 4) and then square it:
   • Half of 4 is 2.
   • Squaring it gives us 2² = 4.
4. Add this squared value (4) to the expression to complete the square:

The expression now looks like this:

x² + 4x + 4

Now, we can factor this expression:

(x + 2)²

Final Answer

Therefore, the number that should be added to the expression x² + 4x to make it a perfect square is 4.