Question

How do you solve `x^2 - 2x = 1` using completing the square?

Answer 1

I found:
`x_1=1+sqrt(2)`
`x_2=1-sqrt(2)`

Explanation:

Add and subtract `1` to get:
`x^2-2xcolor(red)(+1-1)=1`
so:
`x^2-2xcolor(red)(+1)=1color(red)(+1)`
`(x-1)^2=2`
`x-1=+-sqrt(2)`
`x=1+-sqrt(2)`
`x_1=1+sqrt(2)`
`x_2=1-sqrt(2)`