# Derivation of the quadratic formula

We want to find the values of $$x$$ satisfying $$ax^2 + bx + c = 0$$. This is equivalent to

$x^2 + \frac{b}{a} x + \frac{c}{a} = 0.$

“Completing the square” yields

$(x+\frac{b}{2a})^2 - \frac{b^2}{4a^2} + \frac{c}{a} = 0.$