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.

For example:

x^{2 }- 8x +
3 = 0

First you need to get the 3 on the

other side so you subtract 3 from both sides.

x^{2 }- 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.

x^{2 }- 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:

x^{2 }- 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 **+
**

or

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.