Completing the Square

This method is another option you can use to find the solutions of a quadratic function, if you can’t easily factor it. Since it’s very much a step-by-step process, the easiest way to explain this method is to use an example, so let’s do it.

Let’s say we have the function

The first thing we want to do is set the function equal to zero.

Next, we’ll take one half of the coefficient on the x term and square it.

We then add and subtract our result back into the function, so that we don’t change the value of the function.

Now we factor the quantity in parentheses and consolidate the constants.

Now add two to both sides to move the constant to the right side.

Take the square root of both sides to eliminate the exponent on the left. Don’t forget to add the positive/negative sign in front of the square root on the right side.

Finally, add two to both sides of the equation to solve it for x.

This is the same process you’ll follow each time you use this method to solve for the roots of a quadratic function.