To complete the square for the quadratic equation x² + 8x + 4, we follow a systematic approach. Completing the square allows us to transform the quadratic equation into a perfect square trinomial, facilitating easier analysis and solving.
First, let’s isolate the variable terms:
x² + 8x + 4
Next, we focus on the expression x² + 8x. To complete the square, we need to find a number to add that makes this expression a perfect square:
- Take the coefficient of x, which is 8.
- Divide it by 2: 8 / 2 = 4.
- Square this result: 4² = 16.
This means we should add 16 to both sides of the equation. Adding 16, we rewrite the equation as:
x² + 8x + 16 + 4 – 16 = 0
Which simplifies down to:
(x + 4)² – 12 = 0
This is how the equation takes shape into a perfect square. Therefore, the number to add to both sides of the original equation x² + 8x + 4 to complete the square is 16.