# How do you solve 3x^2 = 108?

Jul 7, 2017

$x = \pm 6$

#### Explanation:

$3 {x}^{2} = 108$

$\frac{\cancel{3} {x}^{2}}{\cancel{3}} = \frac{108}{3}$

${x}^{2} = 36$

$x = \sqrt{36}$

$x = \pm 6$

Jul 7, 2017

$x = \pm 6$

#### Explanation:

We have: $3 {x}^{2} = 108$

First, let's divide both sides of the equation by $3$:

$R i g h t a r r o w \frac{3 {x}^{2}}{3} = \frac{108}{3}$

$R i g h t a r r o w {x}^{2} = 36$

Then, let's subtract $36$ from both sides:

$R i g h t a r r o w {x}^{2} - 36 = 36 - 36$

$R i g h t a r r o w {x}^{2} - 36 = 0$

The left-hand side of the equation is now in the form of a difference of squares.

We can factorise it in the following way:

$R i g h t a r r o w \left(x + 6\right) \left(x - 6\right) = 0$

Using the null factor law:

$\therefore x = \pm 6$

Therefore, the solutions to the equation are $x = - 6$ and $x = 6$.