# How do you solve using the completing the square method 4v^2+ 16v=65?

Follow the steps below to get to $v = - 2 + \frac{9}{2} = \frac{5}{2}$,
$v = - 2 - \frac{9}{2} = - \frac{13}{2}$

#### Explanation:

To complete the square, we first want the set up we have in this problem, that is v terms on one side and the constant on the other.

So first we want a clean ${v}^{2}$ term, so we'll divide through by its coefficient:

$4 {v}^{2} + 16 v = 65$

${v}^{2} + 4 v = \frac{65}{4}$

Now we take the $v$ coefficient, divide by 2, then square it and add it to both sides:

${\left(\frac{4}{2}\right)}^{2} = {2}^{2} = 4$

${v}^{2} + 4 v + 4 = \frac{65}{4} + 4$

Now we convert the left side of the equation to a square (and simplify the right):

${\left(v + 2\right)}^{2} = \frac{65}{4} + \frac{16}{4} = \frac{81}{4}$

Now take the square root of both sides:

$v + 2 = \pm \sqrt{\frac{81}{4}} = \pm \frac{9}{2}$

And finally solve for $v$:

$v = - 2 \pm \frac{9}{2}$

$v = - 2 + \frac{9}{2} = \frac{5}{2}$
$v = - 2 - \frac{9}{2} = - \frac{13}{2}$