Solve the Quadratic Equation by Factorization: 5x² − 3x − 2 = 0

Question: Solve the following quadratic equation by factorization:

$$ 5x^2-3x-2=0 $$

Solution

$$ 5x^2-5x+2x-2=0 $$

$$ 5x(x-1)+2(x-1)=0 $$

$$ (x-1)(5x+2)=0 $$

Either

$$ x-1=0 $$

$$ x=1 $$

or

$$ 5x+2=0 $$

$$ x=-\frac{2}{5} $$

Hence,

$$ \boxed{x=1,\ -\frac{2}{5}} $$