# How do you solve the quadratic equation #(3x - 9)^2 = 12# by the square root property?

##### 1 Answer

Aug 31, 2015

#### Answer:

#### Explanation:

The *square root property* tells you that if

#color(blue)(x = +- sqrt(n))#

You can use

#[3(x-3)]^2 = 3^2 * (x-3)^2 = 9 * (x-3)^2#

The equation can thus be written as

#(color(red)(cancel(color(black)(9))) * (x-3)^2)/color(red)(cancel(color(black)(9))) = 12/9#

#(x-3)^2 = 4/3#

The square root property tells you that

#x - 3 = +- sqrt(4/3)#

#x - 3 = +- 2/sqrt(3) = +- (2sqrt(3))/3#

This means that you get

#x = 3 +- (2sqrt(3))/3#

The two solutions to the equation will be

#x_1 = 3 + (2sqrt(3))/3" "# and#" "x_2 = 3 - (2sqrt(3))/3#