Question

How do you solve `k^2-6k+8=0` by completing the square?

Answer 1

`k=2" or "k=4`

Explanation:

`"subtract 8 from both sides"`

`k^2-6k=-8`

`k^2+2(-3)k color(red)(+9)=-8color(red)(+9)`

`(k-3)^2=1`

`color(blue)"take square root of both sides"`

`k-3=+-1larrcolor(blue)"note plus or minus"`

`k=3+-1`

`k=3-1=2" or "k=3+1=4`

Answer 2

`k=4, k=2`

Explanation:

First lets complete the square:

`k^2-6k+8=0`

`rArr (k-3)^2-9+8=0`

`therefore` `(k-3)^2=-1`

`rArr (k-3)^2=1`

`k-3=pmsqrt1`

`k=3pm1`

`k=4, k=2`