# How do you solve #X + sqrt( X + 5) = 7#?

##### 2 Answers

We can write it as follows

The only acceptable solution is x=4

Rearrange, square both sides and solve the resulting quadratic to find two possible solutions, one of which is spurious and the other a solution of the original equation:

#### Explanation:

First subtract

Then square both sides to get:

Note that squaring both sides may have introduced a spurious solution, so we need to check later.

Next subtract

Now

which is zero when

Substituting these into the left hand side of the original equation we find:

(Note: