Question

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

Answer 1

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

Explanation:

The square root property tells you that if `x^2` is equal to a positive number `n`, then you have

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

You can use `3` as a common factor to rewrite the expression that's being squared like this

`[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`