# How do you solve #4-x=sqrt(x-4)#?

##### 1 Answer

#### Answer:

#### Explanation:

**The easy way**

When

So the only solution is

**The normal way**

Square both sides of the equation to get:

#16-8x+x^2 = (4-x)^2 = (sqrt(x-4))^2 = x - 4#

Note that squaring both sides of an equation may introduce spurious solutions (as it does in this case).

Subtract

#x^2-9x+20 = 0#

This factors as:

#(x-4)(x-5) = 0#

So

Then check the solutions:

If

If

Note that this happens because numbers have two square roots. When you square both sides of an equation you throw away some information.