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

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Answer 1 · 2015-08-31T23:35:35

$x = 3 \pm \frac{2 \sqrt{3}}{3}$ $x = 3 +- (2sqrt(3))/3$

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

$x = \pm \sqrt{n}$ $color(blue)(x = +- sqrt(n))$

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

${[3 (x - 3)]}^{2} = 3^{2} \cdot {(x - 3)}^{2} = 9 \cdot {(x - 3)}^{2}$ $[3(x-3)]^2 = 3^2 * (x-3)^2 = 9 * (x-3)^2$

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(3x - 9)^2 = 12 by the square root property?