To complete the square for the quadratic expression x² + 6x – 5, we need to turn the expression into a perfect square trinomial.
The first step is to take the coefficient of the linear term (which is 6 in this case), divide it by 2, and then square the result. So, we compute:
- Divide by 2: 6 / 2 = 3
- Square it: 3² = 9
Now, we need to add this number (9) to both sides of the equation to maintain equality. This gives us:
x² + 6x + 9 – 5 = 9
By doing this, we can rearrange the left side as:
(x + 3)² – 5 = 9
So, the number that should be added to both sides is 9. This helps us to rewrite the equation in a form that makes it easier to solve or analyze graphically.