Question

How do you solve `(x-6)^2 = 25`?

Answer 1

`x=1` or `x=11`

Explanation:

Rewriting `(x-6)^2=25`
as
`(x-6)^2-5^2=0`

we see the left side is the difference of squares with factors:
`((x-6)+5)*((x-6)-5) = 0`

Either
#{: (,(x-6)+5 = 0, ," or ",,(x-6)-5=0), (rArr,x-1=0, , , ,x-11=0), (rArr,x=1, ," or ", ,x=11) :}#