Question

How do you solve the equation `x^2-8x+11=0` by completing the square?

Answer 1

`x=4+sqrt5` and
`x=4-sqrt5`

Explanation:

`x^2-2(x)(4)+(4)^2-(4)^2+11` add and subtract `(4)^2`
`(x-4)^2-5=0`
`(x-4)^2=5`
taking sq root both sides`sqrt((x-4)^2)=sqrt5`
`x-4=+-sqrt5`
`x=4+-sqrt5`

Therefore
`x=4+sqrt5` and
`x=4-sqrt5`