Question

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

Answer 1

Write it as:
`x^2-2x=-6`
Add and subtract `1`;
`x^2-2x+1-1=-6`
`x^2-2x+1=-6+1`
`(x-1)^2=-5`
So:
`x-1=+-sqrt(-5)`
`x=1+-isqrt(5)`
These are two Complex Solutions where `i=sqrt(-1)`