squares

mslex1234

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Nov 9, 2010
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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
 
x2 + 5 = 21.\displaystyle x^2 \ + \ 5 \ = \ 21.

x2 = 215 =16.\displaystyle x^2 \ = \ 21-5 \ =16.

x2 = 16.\displaystyle \sqrt{x^2} \ = \ \sqrt{16}.

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

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