Question

Solve the following equation by factorization:

$\sqrt{2}{x}^2-3x-2\sqrt{2}=0$

Answer 1

Factorizing the equation:

We know, $\sqrt{2}{x}^2-3x-2\sqrt{2}=0$

$$\begin{gathered} \Rightarrow \sqrt{2}{x}^2-4x+x-2\sqrt{2}=0 \\ \Rightarrow \sqrt{2}x(x-2\sqrt{2})+1(x-2\sqrt{2})=0 \\ \Rightarrow (\sqrt{2}x+1)(x-2\sqrt{2})=0 \end{gathered}$$

Use the zero product property to find the value of $x$.

$\Rightarrow \sqrt{2}x+1=0$ or, $x-2\sqrt{2}=0$

$\Rightarrow x=-\frac{1}{\sqrt{2}}$ or, $x=2\sqrt{2}$

Therefore, the values are $x=-\frac{1}{\sqrt{2}}$ or, $x=2\sqrt{2}$.