Question

How do you solve `(x-3)^2=36`?

Answer 1

`x=9 and x=-3`

Explanation:

`(x-3)^2 = 36`

`(x-3)^2 = 6^2`

`sqrt ((x-3)^2)` = 6

`+- (x-3)`= 6

either,
taking +,
`+ (x-3) =6`
`x-3=6`
`x=6+3`
So,
`x=9`

Or,
Taking -,
`-(x-3) =6`
`-x +3 =6`
`-x = 6-3`
`-x= 3`
So,
`x= -3`

Answer 2

I found:
`x_1=9`
`x_2=-3`

Explanation:

You can take the square root of both sides and get:
`(x-3)=+-sqrt(36)`
`x=3+-6`
so you have two possibilities:
`x_1=3+6=9`
`x_2=3-6=-3`
Both work when inserted into your original equation.