Question

Solve the quadratic equation $5x^2-6x-2=0$ by completing the square.

Answer 1

Given quadratic equation is $5x^2-6x-2=0$.

$\to x^2-\frac{6}{5}x-\frac{2}{5}=0$ (Divide on both sides by 5)

$\to x^2-2\left(\frac{3}{5}\right)x+\frac{9}{25}=\frac{9}{25}+\frac{2}{5}$ (add ${\left(\frac{3}{5}\right)}^2=\frac{9}{25}$ on both sides)

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

$\to x-\frac{3}{5}=\pm \sqrt{\frac{19}{25}}$ (take square root on both sides)

Thus, we have $x=\frac{3}{5}\pm \frac{\sqrt{19}}{5}=\frac{3\pm \sqrt{19}}{5}$.

Hence, the solution set is $\{\frac{3+\sqrt{19}}{5},\frac{3-\sqrt{19}}{5}\}$.