Question

Find the roots of the equation $5x^2-6x-2=0$ by the method of completing the square.

Answer 1

We have,

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

$x^2-\frac{6}{5}x-\frac{2}{5}=0$

$x^2-\frac{6}{5}x=\frac{2}{5}$

$x^2-2\left(\frac{3}{5}\right)x+(\frac{3}{5}{)}^2=\frac{2}{5}+(\frac{3}{5}{)}^2$

$(x-\frac{3}{5}{)}^2=\frac{19}{25}$

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

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