Question

Find the roots of the equations by the method of completing the square.
$x^2-10x+9=0$

Answer 1

$x^2-10x+9=0$

$\Rightarrow$ Here, $a=1,b=-10,c=9$

$\Rightarrow$ $x^2-10x=-9$

Now, ${\left(\frac{b}{2}\right)}^2={\left(\frac{10}{2}\right)}^2=25$

Adding $25$ on both sides,

$\Rightarrow$ $x^2-10x+25=-9+25$

$\Rightarrow$ $(x-5{)}^2=16$

$\Rightarrow$ $x-5=\pm 4$

$\Rightarrow$ $x-5=4$ and $x-5=-4$

$\therefore$ $x=9$ and $x=1$