1. Convert the given equation `x^2+6x+9` into perfect square form
Solution:
`x^2+6x+9`
`=1 (x^2+6x+9)`
The coefficient of the x is `6`, so now we divide this by 2 : `(6 -: 2 = 3)`
and square it `(3)^2=9`. So we add and subtract `9`
`=1( x + 3 )^2`
2. Convert the given equation `9x^2+6x+1` into perfect square form
Solution:
`9x^2+6x+1`
`=9 (x^2+(2x)/3+1/9)`
The coefficient of the x is `2/3`, so now we divide this by 2 : `(2/3 -: 2 = 1/3)`
and square it `(1/3)^2=1/9`. So we add and subtract `1/9`
`=9( x + 1/3 )^2`
3. Convert the given equation `3x^2+5x+2` into perfect square form
Solution:
`3x^2+5x+2`
`=3 (x^2+(5x)/3+2/3)`
The coefficient of the x is `5/3`, so now we divide this by 2 : `(5/3 -: 2 = 5/6)`
and square it `(5/6)^2=25/36`. So we add and subtract `25/36`
`=3 (x^2+(5x)/3 + 25/36 - 25/36 + 2/3)`
`=3 [(x^2+(5x)/3+25/36) -1/36]`
`=3[( x + 5/6 )^2 -1/36 ]`
This material is intended as a summary. Use your textbook for detail explanation.
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