Question

The quadratic equation $5x^2-6x-2=0,$ can be simplified to

• A. ${\left(x-\frac{3}{5}\right)}^2=\frac{19}{25}$
• B. $5{\left(x-\frac{3}{5}\right)}^2=\frac{19}{25}$
• C. ${\left(x-19\right)}^2=0$
• D. ${\left(x-2\right)}^2=\frac{19}{5}$

Answer 1

The correct option is A ${\left(x-\frac{3}{5}\right)}^2=\frac{19}{25}$

Given: $5x^2-6x-2=0$
Taking $5$ common on both sides of the equation, we get:
$x^2-\frac{6}{5}x-\frac{2}{5}=0$
Now, comparing the equation with $(a-b{)}^2=a^2-2ab+b^2,$ we get:
$a=x,$ thus the equation becomes:
$(x-b{)}^2=x^2-2bx+b^2$

Now, comparing we get: $b=\frac{3}{5}$
$\Rightarrow x^2-\frac{6}{5}x-\frac{2}{5}=0\Rightarrow x^2-\frac{6}{5}x+\frac{9}{25}-\frac{9}{25}-\frac{2}{5}=0\Rightarrow {(x-\frac{3}{5})}^2-\frac{19}{25}=0\Rightarrow {(x-\frac{3}{5})}^2=\frac{19}{25}$