Question:
Solve the following quadratic equations by factorization:
$25 x(x+1)=-4$
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 $x=\frac{-4}{5}$.