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The area of a square, in square units, is 38 more than 10 times the length of a side of the square, in units.
Find all possible values for the side length of the square.

 May 20, 2024
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This isn't hard to do, we just have to set up an equation. 

 

First, let s be the sidenlength of a equation. 

 

\(s^2 = 10s + 38 \\ s^2 - 10s = 38 \\ s^2 -10s + 25 = 38 + 25\)

\((s - 5)^2 = 63 \)

\(s - 5 = \sqrt{63}\)

\(s = \sqrt{63} + 5\)

 

The other possible equation would get a negative value, but a sidlength can't be negative, so we reject that possibility. 

 

So we have \(s = \sqrt{63} + 5\)

 

Thanks! :)

 May 20, 2024

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