Question

How do you solve the equation `(x-12)^2 = 121` using the square root property?

Answer 1

The solutions are
`color(blue)(x=1, x=23`

Explanation:

The square root property involves taking the square root of both the terms on either side of the equation.

Applying the same to the given equation:

`sqrt((x-12)^2)=sqrt(121`

(`sqrt121= color(blue)(+-11`)

So,
`sqrt((x-12)^2)=color(blue)(+-11`

`(x-12)=color(blue)(+-11`

Solution 1:
`x-12 = +11`
Isolating `x`
`x-12 +color(blue)(12)= +11+color(blue)(12)`
`color(blue)(x=23`

Solution 2:
`x-12 = -11`
Isolating `x`
`x-12 +color(blue)(12)= -11 +color(blue)(12)`
`color(blue)(x=1`