# How do you solve x^2-16x+7=0 using the quadratic formula?

Aug 22, 2016

The two solutions are $x = 15.55$ and $x = 0.45$

#### 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 $- 16 x$, and $c$ is a number by itself and in this case it is 7.

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

$x = \frac{- \left(- 16\right) \pm \sqrt{{\left(- 16\right)}^{2} - 4 \left(1\right) \left(7\right)}}{2 \left(1\right)}$

$x = \frac{16 \pm \sqrt{256 - 28}}{2}$

$x = \frac{16 \pm \sqrt{228}}{2}$

For these type of problems, you will obtain two solutions because of the $\pm$ part. So what you want to do is add 16 and $\sqrt{228}$ together and divide that by 2:

$x = \frac{16 + \sqrt{228}}{2}$
$x = \frac{31.10}{2} = 15.55$

Now, we subtract $\sqrt{228}$ from 16 and divide by 2:

$x = \frac{16 - \sqrt{228}}{2}$
$x = \frac{0.90}{2} = 0.45$

Therefore, the two possible solutions are:
$x = 15.55$ and $x = 0.45$