Problem of the Week

Updated at Oct 26, 2020 11:51 AM

For this week we've brought you this equation problem.

How can we solve the equation \({(\frac{u}{5}+2)}^{2}-6=\frac{19}{25}\)?

Here are the steps:



\[{(\frac{u}{5}+2)}^{2}-6=\frac{19}{25}\]

1
Add \(6\) to both sides.
\[{(\frac{u}{5}+2)}^{2}=\frac{19}{25}+6\]

2
Simplify  \(\frac{19}{25}+6\)  to  \(\frac{169}{25}\).
\[{(\frac{u}{5}+2)}^{2}=\frac{169}{25}\]

3
Take the square root of both sides.
\[\frac{u}{5}+2=\pm \sqrt{\frac{169}{25}}\]

4
Simplify  \(\sqrt{\frac{169}{25}}\)  to  \(\frac{\sqrt{169}}{\sqrt{25}}\).
\[\frac{u}{5}+2=\pm \frac{\sqrt{169}}{\sqrt{25}}\]

5
Since \(13\times 13=169\), the square root of \(169\) is \(13\).
\[\frac{u}{5}+2=\pm \frac{13}{\sqrt{25}}\]

6
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[\frac{u}{5}+2=\pm \frac{13}{5}\]

7
Break down the problem into these 2 equations.
\[\frac{u}{5}+2=\frac{13}{5}\]
\[\frac{u}{5}+2=-\frac{13}{5}\]

8
Solve the 1st equation: \(\frac{u}{5}+2=\frac{13}{5}\).
\[u=3\]

9
Solve the 2nd equation: \(\frac{u}{5}+2=-\frac{13}{5}\).
\[u=-23\]

10
Collect all solutions.
\[u=3,-23\]

Done
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