Mammoth Memory

Completing the square - example 1

Complete the square `x^2-6x+8=0`

Quick sketch


Complete the square and split the square into quarters using x square

Fill the square in with the next term

Is the same as

This table is the same as the one above

Fill in the table

Fill in the table multiplying the y axis by the x axis

Is the same as

This table will mean the same thing as the one above


This is the same as `(x-3)^2`


If you add up each area we get:




Originally we had   `x^2-6x+8=0`

Now we have          `x^2-6x+9=0`


Always plot this on a number line

Use the number line to work out the difference between the original number and the new number

The number line will help you remember original number `-`  new number

`8-9=-1`  (We need `-1` )

So                        `x^2-6x+8=0`

Is the same as  `(x-3)^2-1=0`


Which can now be solved





(Don't forget the root of anything can be + or -)



`x=3+1`   or   `x=3-1`

`x=4`   or   `x=2`


Now check


If `x=4`       `4^2-6times4+8=0`

`16-24+8=0`   Which is correct

If `x=2`       `2^2-6times2+8=0`

`4-12+8=0`     Which is correct



The roots of `x^2-6x+8=0`  are `x=4`  and `x=2`