# How do you solve x^2-8x+3=0 using the quadratic formula?

Aug 22, 2016

$x = 7.605$ and $x = 0.395$

#### Explanation:

I'll show the quadratic formula down below so we can use that as a reference:

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 $- 8 x$, and $c$ is a number by itself. It would be 3 for this question.

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

$x = \frac{- \left(- 8\right) \pm \sqrt{{\left(- 8\right)}^{2} - 4 \left(1\right) \left(3\right)}}{2 \left(1\right)}$

$x = \frac{8 \pm \sqrt{64 - 12}}{2}$

$x = \frac{8 \pm 7.21}{2}$

For these type of problems, you will obtain two solutions because of the $\pm$ part. So what you want to do is add 8 and 7.21 together and divide that by 2:

$x = \frac{8 + 7.21}{2}$
$x = \frac{15.21}{2} = 7.605$

Now, we subtract 7.21 from 8 and divide by 2:

$x = \frac{8 - 7.21}{2}$
$x = \frac{0.79}{2} = 0.395$

Therefore, the two possible solutions are:
$x = 7.605$ and $x = 0.395$