Solve the Quadratic Equation by Factorization: 25x(x + 1) = -4

Question: Solve the following quadratic equation by factorization:

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

Solution

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

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

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

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

Either

$$ 5x+4=0 $$

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

or

$$ 5x+1=0 $$

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

Hence,

$$ \boxed{x=-\frac{4}{5},\ -\frac{1}{5}} $$