Question

Solve each of the following equation by using the method of completing the square:
$\sqrt{2}{x}^2-3x-2\sqrt{2}=0$

Answer 1

Given,

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

$\sqrt{2}{x}^2-4x+x-2\sqrt{2}=0$

$\sqrt{2}x(x-2\sqrt{2})+1(x-2\sqrt{2})=0$

$(x-2\sqrt{2})(\sqrt{2}x+1)=0$

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