Question

Find the roots of the following quadratic equation (if they exist) by the method of completing the square.
$x^2-4ax+4a^2-b^2=0$

Answer 1

$x^2-4ax+4a^2-b^2=0$

Completing the square :

$\Rightarrow x^2-2\left(2a\right)x+(2a{)}^2=b^2$

$\Rightarrow (x-2a{)}^2=b^2$

$\Rightarrow x=\pm b+2a$

$\Rightarrow x=2a+b$ or $x=2a-b$