Completing the Square
By following these simple directions
you can learn to solve for X
by completing the square
and then take a quiz
at the end to make sure you got it.
If the problem that you start out with is
not a perfect square to begin with
(the product of two identical binomials)
completing the square will help you.
x2 - 8x + 3 = 0
First you need to get the 3 on the
other side so you subtract 3 from both sides.
x2 - 8x = -3
After that you take the number next to the single x (8)
and divide it by 2 and get 4.
Then you put (x -4)2 under the problem
because you will need that later.
x2 - 8x + ___ = -3 + ____
To fill in the 2 blanks on the top row
you square 4 to get 16.
If you do something to one side
you have to do it to the other.
After adding 16 to both sides you will get:
x2 - 8x + 16 = -3 + 16
(x - 4)2 = 13
Now you have to take the square root
of both sides to get:
x - 4 = ±
Then you add 4 to both sides
and end up with:
x = 4 +
x = 4 -
By following those simple instructions on how to complete the square you should be able to do any kind of completing the square problem.
Click here to take a Quiz!