# squares

#### mslex1234

##### New member
I have a test tomorrow and we ran out of time in class today...the problem I am having is...

If 5 is added to the square of a number, the result is 21. Find the number.

x(x+5)=21

I think the answer is 4,-4 but do not really know how to work the problem out! Please help. And thank you in advanced. I am a bit frustrated...

The way I did it is...21-5 is 16, the square of 16 is 4. which makes it 4, -4

#### BigGlenntheHeavy

##### Senior Member
$$\displaystyle x^2 \ + \ 5 \ = \ 21.$$

$$\displaystyle x^2 \ = \ 21-5 \ =16.$$

$$\displaystyle \sqrt{x^2} \ = \ \sqrt{16}.$$

$$\displaystyle |x| \ = \ 4, \ \implies \ x \ = \ 4 \ or \ x \ = \ -4.$$

$$\displaystyle Note: \ By \ definition \ \sqrt{16} \ = \ 4, \ not \ -4.$$

#### mslex1234

##### New member
thank you so much for the quick response!