# How do you solve u^2-4u=2u+35 by completing the square?

Feb 20, 2017

$u = 3 + \sqrt{44}$ and $3 - \sqrt{44}$

#### Explanation:

First, subtract $2 u$ on both sides.

${u}^{2} - 6 u = 35$

Now find ${\left(\frac{b}{2 a}\right)}^{2}$ where $a$ is the coefficient in front of ${u}^{2}$ and $b$ is the coefficient in front of $u$ (so $b = - 6$ and $a = 1$ in this case)

${\left(- \frac{6}{2 \left(1\right)}\right)}^{2} = 9$

Now, complete the square by adding both sides by 9.

${u}^{2} - 6 u + 9 = 44$

Rewrite the left side:

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

Solve for u. Remember that taking the square root of both sides will give you a positive and negative number.

$\left(u - 3\right) = \sqrt{44}$ and $- \sqrt{44}$

$u = 3 + \sqrt{44}$ and $3 - \sqrt{44}$