To complete the square for the quadratic expression x² + 7x + 4, we first focus on the x² + 7x part.
1. Take the coefficient of x, which is 7, and divide it by 2. This gives us 3.5.
2. Next, square 3.5 to determine the number to add. Squaring 3.5 gives us 12.25.
3. Now we add this number, 12.25, to both sides of the equation. So, if we add 12.25 to the left side where our quadratic is, we also need to add it to the other side to keep the equation balanced.
Thus, the number you would add to both sides to complete the square is 12.25.