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

Aug 13, 2015

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 $x$
$x - 12 + \textcolor{b l u e}{12} = + 11 + \textcolor{b l u e}{12}$
color(blue)(x=23

Solution 2:
$x - 12 = - 11$
Isolating $x$
$x - 12 + \textcolor{b l u e}{12} = - 11 + \textcolor{b l u e}{12}$
color(blue)(x=1