Question

how to factor 2x^2 - 9 = 0

Answer 1

The given expression is

$2x^2-9=0$

First, we add 9 on each side

$\begin{gathered} 2x^2-9+9=0+9 \\ 2x^2=9 \end{gathered}$

Then, we divide the equation by 2

$\begin{gathered} \frac{2x^2}{2}=\frac{9}{2} \\ x^2=\frac{9}{2} \\ x=\pm\sqrt[]{\frac{9}{2}} \\ x=\frac{3}{\pm\sqrt[]{2}} \end{gathered}$

Hence, the solutions are

$\begin{gathered} x=\frac{3}{\sqrt[]{2}} \\ x=\frac{3}{-\sqrt[]{2}} \end{gathered}$

As factors, we have

$(x-\frac{3}{\sqrt[]{2}})(x+\frac{3}{\sqrt[]{2}})$