To complete the square for the equation x² + 8x + 4, we need to focus on the x² + 8x part. The goal is to form a perfect square trinomial from this expression.
To find the number that needs to be added, we take the coefficient of x (which is 8), divide it by 2, and then square the result:
Step 1: 8 ÷ 2 = 4
Step 2: 4² = 16
This means we need to add 16 to both sides of the equation. By doing so, we can rewrite the equation as:
x² + 8x + 16 = 16 – 4
That simplifies to:
(x + 4)² = 12
Therefore, the number that should be added to both sides of the equation to complete the square is 16.