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

Aug 31, 2015

$x = 3 \pm \frac{2 \sqrt{3}}{3}$

#### Explanation:

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

$\textcolor{b l u e}{x = \pm \sqrt{n}}$

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

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

The equation can thus be written as

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} \cdot {\left(x - 3\right)}^{2}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}}} = \frac{12}{9}$

${\left(x - 3\right)}^{2} = \frac{4}{3}$

The square root property tells you that

$x - 3 = \pm \sqrt{\frac{4}{3}}$

$x - 3 = \pm \frac{2}{\sqrt{3}} = \pm \frac{2 \sqrt{3}}{3}$

This means that you get

$x = 3 \pm \frac{2 \sqrt{3}}{3}$

The two solutions to the equation will be

${x}_{1} = 3 + \frac{2 \sqrt{3}}{3} \text{ }$ and $\text{ } {x}_{2} = 3 - \frac{2 \sqrt{3}}{3}$