# How do you solve #sqrt(x + 10) = x - 2#?

##### 1 Answer

The only solution is

See explanation below about *arithmetic square root*.

#### Explanation:

First of all, we assume that the equation should be solved for *real* numbers *complex*, *integer*, etc.) is usually specified explicitly.

When square root is involved and we plan to raise both sides of an equation to the power of 2 to get rid of it, we have to start from the domain where the equation can have sense. In this case, the set of real numbers where the solution should exist is defined as

Another restriction is related to the fact that, when we use a notation *arithmetic square root*, that is a **non-negative** number, square root of which is

This agreement necessitates that the right side of an equation must be non-negative, that is

Combination of two restrictions,

With this restriction in mind, let's square the equation:

After opening the parenthesis it's transformed into

Two roots of this equation are

Only the first solution satisfy the initial restriction

CHECK

For

and the right side is

This is an identity