Question

Using the Completing Square Method convert the following quadratic equation in the form of $(x+p{)}^2=q$ and then find out its roots.

$5x^2-6x-2=0$

Answer 1

$5x^2-6x-2=0$

$\Rightarrow (\sqrt{5}x-\frac{3}{\sqrt{5}}{)}^2=2+\frac{9}{5}$

$\Rightarrow (\sqrt{5}x-\frac{3}{\sqrt{5}}{)}^2=\frac{19}{5}$

$\Rightarrow \sqrt{5}x-\frac{3}{\sqrt{5}}=\pm \frac{\sqrt{19}}{\sqrt{5}}$

$\Rightarrow x=\frac{\pm \sqrt{19}+3}{5}$

$\therefore x=\frac{3\pm \sqrt{19}}{5}$