To complete the square, your goal is to make a perfect trinomial. For example:
To make things easier, let's add some parentheses to the equation.
You need to add a constant into the parentheses to create a perfect trinomial. To find this constant, use this formula:
This is where things can get a little confusing. Because you are adding a number on one side of the equation, and not the other side, you need to balance it out on the same side.
As you can see, you've created your perfect trinomial while also not unbalancing your equation. Now you can factor and simplify!
To complete the square, we need to find a value that makes
To solve for the missing component, we need to follow these steps:
1) take the middle term,
2) square this solution
Now, let's add this to the equation. REMEMBER in an equation, we can add whatever we want, but we must also add it to the other side:
Now we have our solution!