# How do you solve v^ { 2} - 6v = 35 by completing the square?

Apr 17, 2017

By completing the square, we see that

${v}^{2} - 6 v - 35 = {v}^{2} - 6 v + 9 - 44 = {\left(v - 3\right)}^{2} - 44$

so in order to solve it we can solve

${\left(v - 3\right)}^{2} = 44$

By setting $x = v - 3$, we can solve ${x}^{2} = 44 R i g h t a r r o w x = 2 \pm \sqrt{11}$, hence $v - 3 = \sqrt{11} R i g h t a r r o w v = 3 + \sqrt{11}$

Apr 17, 2017

$v = 2 \sqrt{11} + 3$

#### Explanation:

Completing the square is a process where one would manipulate the polynomial such that it could be factored into the form (variable +/- number) squared.

The trick to finding the third term in the polynomial is ${\left(\frac{b}{2}\right)}^{2}$. Thus, for this equation, we want the left side to be ${v}^{2} - 6 v + 9$.

With that in mind, we add 9 to both sides, and simplify.
${v}^{2} - 6 v + 9 = 44$
${\left(v - 3\right)}^{2} = 44$

Now we can take the square root of both sides, and solve for v.
$v - 3 = \sqrt{44}$
$v = \sqrt{44} + 3$
$v = 2 \sqrt{11} + 3$