Question

How do you solve `x^2 - 2x +1=0`?

Answer 1

`x=1`

Explanation:

Given
`color(white)("XXXX")` `x^2-2x+1 = 0`
Factor the left side to get
`color(white)("XXXX")` `(x-1)(x-1) = 0`
From which it follows that
`color(white)("XXXX")` `(x-1) = 0`
and
`color(white)("XXXX")` `x=1`

Answer 2

This is a quadratic equation, that you can factorise.

Explanation:

Find a pair of numbers that add up to `-2x` and multiplies to `+1`

Maybe you'll see that that would be `-1and-1`

Now you can factorise:
`=(x-1)*(x-1)=0->x-1=0->x=1`

Check your answer:
`1^2-2*1+1=0`
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