Question

How do you solve `sqrt(5(x+3))=10` and find any extraneous solutions?

Answer 1

Distribute inside the radical, and then square both sides.

Explanation:

`sqrt(5(x + 3)) = 10`

`(sqrt(5x + 15))^2 = 10^2`

`5x + 15 = 100`

`5x = 85`

`x = 17`

Since this is a radical equation, we must always check our answer back in the original equation to verify that there are no extraneous solutions. Checking, we find that `x = 17` satisfies our equation; the solution set is `{x = 17}`.

Hopefully this helps!