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

Question

2349 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-31T23:35:35

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

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 $" "x_2 = 3 - (2sqrt(3))/3$

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