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

Question

1379 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-22T21:42:19

Please see the explanation.

The restriction that I would add is $x<= 25/2$

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

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.

Add 2x-64 to both sides:

$2x = 25-64$

$2x = -39$

$x = -39/2$

Check:

$5=13-sqrt(25-2(-39/2))$

$5 = 13 - sqrt(64)$

$5 = 5$

This checks.

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