Problem of the Week

Updated at Aug 1, 2022 12:33 PM

This week we have another equation problem:

How can we solve the equation \({(\frac{n}{5}-3)}^{2}-3=1\)?

Let's start!



\[{(\frac{n}{5}-3)}^{2}-3=1\]

1
Add \(3\) to both sides.
\[{(\frac{n}{5}-3)}^{2}=1+3\]

2
Simplify  \(1+3\)  to  \(4\).
\[{(\frac{n}{5}-3)}^{2}=4\]

3
Take the square root of both sides.
\[\frac{n}{5}-3=\pm \sqrt{4}\]

4
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\frac{n}{5}-3=\pm 2\]

5
Break down the problem into these 2 equations.
\[\frac{n}{5}-3=2\]
\[\frac{n}{5}-3=-2\]

6
Solve the 1st equation: \(\frac{n}{5}-3=2\).
\[n=25\]

7
Solve the 2nd equation: \(\frac{n}{5}-3=-2\).
\[n=5\]

8
Collect all solutions.
\[n=25,5\]

Done
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