Completing the square - example 1
Complete the square x2-6x+8=0
Remember
Is the same as
Fill in the table
Is the same as
NOTE:
This is the same as (x-3)2
If you add up each area we get:
x2-3x-3x+9
x2-6x+9
Originally we had x2-6x+8=0
Now we have x2-6x+9=0
Always plot this on a number line
The number line will help you remember original number - new number
8-9=-1 (We need -1 )
So x2-6x+8=0
Is the same as (x-3)2-1=0
Which can now be solved
(x-3)2-1=0
(x-3)2=1
x-3=±√1
(Don't forget the root of anything can be + or -)
x-3=±1
x=3±1
x=3+1 or x=3-1
x=4 or x=2
Now check
x2-6x+8=0
If x=4 42-6×4+8=0
16-24+8=0 Which is correct
If x=2 22-6×2+8=0
4-12+8=0 Which is correct
Answer:
The roots of x2-6x+8=0 are x=4 and x=2



