In this video, we are going to look at how to complete the square. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.
For example:
If we are given
we can multiply it out to get
Here we have
and we want c to be some number so that when factored, both binomials are exactly the same. To figure out what this c value will be, we will do the following:
So in this case,
is the same as
or 
In this case, c needs to be 4.
If we had something like
then
so
If we had to factor from here, then the two terms are whatever 
was. When we factor this we get
Example of Completing the Square
Example 1
To figure out what this c value will be, we will do the following:
Subsitute the value of 
The answer will be
Example 2
To figure out what this c value will be, we will do the following:
Subsitute the value of
The answer will be
Video-Lesson Transcript
Let’s go over solving equations by factoring.
The first thing to note here is that we have a quadratic and it’s equal to zero.
So we have to make sure that the right side is zero.
Now, let’s factor this.
Draw two parenthesis and write 
on each.
Then find two numbers that will add up to 
and when multiplied will be equal to 
.
When can two numbers when multiplied be equal to zero?
One of them has to be zero. Because of zero product property.
So we have to come up with one of these terms be zero.
Meaning 
or 
Either of the two should be zero.
,
,
and
,
,
So we have two solutions:
{
}
We usually use the brackets not the parenthesis.
Let’s have another one
Again, let’s factor this.
Draw two parenthesis and in each parenthesis.
Then think of two numbers that when you add up will equal and when multiplied will equal 
.
,
,
,
,
and
,
,
Our two solutions are
{
}
Take a look at this one:
Notice that the right side is not zero.
So we have to make it zero.
,
Now we can factor this out.
,
Let’s solve for
,
,
and
,
,
So our solution set is
{
}
