Question

Solve each of the following equation by using the method of completing the square:
$5x^2+6x-2=0$ ?

Answer 1

Given,

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

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

add and subtract ${\left(\frac{3}{5}\right)}^2$, we get

$x^2+\frac{6}{5}x-\frac{2}{5}+{\left(\frac{3}{5}\right)}^2-{\left(\frac{3}{5}\right)}^2=0$

$x^2+\frac{6}{5}x+{\left(\frac{3}{5}\right)}^2-\frac{2}{5}-{\left(\frac{3}{5}\right)}^2=0$

${(x+\frac{3}{5})}^2-\frac{2}{5}-\frac{9}{25}=0$

${(x+\frac{3}{5})}^2=\frac{2}{5}+\frac{9}{25}=\frac{19}{25}$

$\therefore x+\frac{3}{5}=\pm \frac{19}{25}$

$\Rightarrow x=\pm \frac{19}{25}-\frac{3}{5}$

$\therefore x=\frac{19}{25}-\frac{3}{5}=\frac{4}{25}$

$\therefore x=-\frac{19}{25}-\frac{3}{5}=-\frac{34}{25}$