Solve the following quadratic equations by factorization:

Solution:

We have been given

$25 x(x+1)=-4$

$25 x^{2}+25 x+4=0$

$25 x^{2}+20 x+5 x+4=0$

$5 x(5 x+4)+1(5 x+4)=0$

 

$(5 x+1)(5 x+4)=0$

Therefore,

$5 x+1=0$

$5 x=-1$

$x=\frac{-1}{5}$

or,

$5 x+4=0$

$5 x=-4$

$x=\frac{-4}{5}$

Hence, $x=\frac{-1}{5}$ or $x=\frac{-4}{5}$.