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} (2x^2)/(2)=(9)/(2) \\ x^2=(9)/(2) \\ x=\pm\sqrt[]{(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}})`