We know how to solve equations like . We do this by factoring. If we factor we will get

so

Not all trinomials are factorable. Sometimes we also just can’t figure out how to factor a trinomial. What if we couldn’t figure out how to factor ? We can’t find 2 numbers that multiply to and add to . So how are we possibly going to solve this equation? We will use the Quadratic Formula

This is how it works. The generic case looks like . So in the case of

We take these numbers and plug them into the following formula

The symbol means that you have to do this twice; once as a plus and once as a minus. This is where your two answers come from. Let’s plug our equation’s numbers into the quadratic formula to find the answers.

Simplify the insides of the radical we get

This can work on any quadratic equation, but the answers may not be so nice.

### 5 Step Process for Quadratic Formula

(Only if you’re having trouble.)

\textbf{Example:} Solve the equation

\textbf{Step 1:} Determine , , and

Step 2: Plug into the quadratic formula

Step 4: Split into 2 problems — plus & minus