Solve the Quadratic Equation by Factorization: 48x² − 13x − 1 = 0

Question: Solve the following quadratic equation by factorization:

$$ 48x^2-13x-1=0 $$

Solution

$$ 48x^2-16x+3x-1=0 $$

$$ 16x(3x-1)+1(3x-1)=0 $$

$$ (3x-1)(16x+1)=0 $$

Either

$$ 3x-1=0 $$

$$ x=\frac{1}{3} $$

or

$$ 16x+1=0 $$

$$ x=-\frac{1}{16} $$

Hence,

$$ \boxed{x=\frac{1}{3},\ -\frac{1}{16}} $$