Find the roots of the following quadratic equations

We have to find the roots of given quadratic equation by the method of completing the square. We have,

$x^{2}-4 a x+4 a^{2}-b^{2}=0$

Now shift the constant to the right hand side,

$x^{2}-4 a x=b^{2}-4 a^{2}$

Now add square of half of coefficient ofon both the sides,

$x^{2}-2(2 a) x+(2 a)^{2}=b^{2}-4 a^{2}+(2 a)^{2}$

We can now write it in the form of perfect square as,

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

Taking square root on both sides,

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

So the required solution of,

$x=2 a \pm b$

$=2 a+b, 2 a-b$