**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 x^{2} = d or (x + c)^{2} = d.

**b. **If it is not in the form of step (a), write it in standard form

ax^{2} + 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.