# How do you solve x^2+3x+2=0 using the quadratic formula?

Dec 26, 2016

The two solutions are $x = - 1$ and $x = - 2$

#### Explanation:

Since this question is given in standard form, meaning that it follows the form: $a {x}^{2} + b x + c = 0$, we can use the quadratic formula to solve for x: I think it's worthwhile to mention that $a$ is the number that has the ${x}^{2}$ term associated with it. Thus, it would be $1 {x}^{2}$ for this question. $b$ is the number that has the $x$ variable associated with it and it would be $3 x$, and $c$ is a number by itself and in this case it is 2.

Now, we just plug our values into the equation like this:

$x = \frac{- \left(3\right) \pm \sqrt{{\left(3\right)}^{2} - 4 \left(1\right) \left(2\right)}}{2 \left(1\right)}$

$x = \frac{- 3 \pm \sqrt{9 - 8}}{2}$

$x = \frac{- 3 \pm \sqrt{1}}{2}$

For these type of problems, you will obtain two solutions because of the $\pm$ part. So what you want to do is add -3 and $\sqrt{1}$ together and divide that by 2:

$x = \frac{- 3 + \sqrt{1}}{2}$
$x = - \frac{2}{2} = - 1$

Now, we subtract $\sqrt{1}$ from -3 and divide that by 2:

$x = \frac{- 3 - \sqrt{1}}{2}$
$x = - \frac{4}{2} = - 2$

Therefore, the two possible solutions are:
$x = - 1$ and $x = - 2$