# How do you solve 5=13-sqrt(25-2x) and identify any restrictions?

Apr 22, 2017

#### Explanation:

The restriction that I would add is $x \le \frac{25}{2}$

5=13-sqrt(25-2x);x<= 25/2

Subtract 13 from both sides:

-8=-sqrt(25-2x);x<= 25/2

Square both sides:

64 = 25 - 2x;x<= 25/2

We can drop the restriction on the next step, because the root is clearly not going to violate it.

$2 x = 25 - 64$

$2 x = - 39$

$x = - \frac{39}{2}$

Check:

$5 = 13 - \sqrt{25 - 2 \left(- \frac{39}{2}\right)}$

$5 = 13 - \sqrt{64}$

$5 = 5$

This checks.