The Quadratic Formula
The solutions of ax + bx + c = 0 are given by
x =
The formula also holds when a < 0. A similar proof would show this, but we will not consider it here.
To solve a quadratic equation:
a. Check for the form x2 = d or (x + c)2 = d.
b. If it is not in the form of step (a), write it in standard form
ax2 + bx + c = 0 with a and b nonzero.
c. Then try factoring.
d. If it is not possible to factor or if factoring seems difficult, use the
quadratic formula.
The solutions of a quadratic equation cannot always be found by
factoring. They can always be found using the quadratic formula.