Problem of the Week

Updated at Mar 30, 2026 1:38 PM

This week we have another equation problem:

How would you solve \(2(2+\frac{5}{{u}^{2}})=\frac{37}{8}\)?

Let's start!



\[2(2+\frac{5}{{u}^{2}})=\frac{37}{8}\]

1
Divide both sides by \(2\).
\[2+\frac{5}{{u}^{2}}=\frac{\frac{37}{8}}{2}\]

2
Simplify  \(\frac{\frac{37}{8}}{2}\)  to  \(\frac{37}{8\times 2}\).
\[2+\frac{5}{{u}^{2}}=\frac{37}{8\times 2}\]

3
Simplify  \(8\times 2\)  to  \(16\).
\[2+\frac{5}{{u}^{2}}=\frac{37}{16}\]

4
Subtract \(2\) from both sides.
\[\frac{5}{{u}^{2}}=\frac{37}{16}-2\]

5
Simplify  \(\frac{37}{16}-2\)  to  \(\frac{5}{16}\).
\[\frac{5}{{u}^{2}}=\frac{5}{16}\]

6
Multiply both sides by \({u}^{2}\).
\[5=\frac{5}{16}{u}^{2}\]

7
Simplify  \(\frac{5}{16}{u}^{2}\)  to  \(\frac{5{u}^{2}}{16}\).
\[5=\frac{5{u}^{2}}{16}\]

8
Multiply both sides by \(16\).
\[5\times 16=5{u}^{2}\]

9
Simplify  \(5\times 16\)  to  \(80\).
\[80=5{u}^{2}\]

10
Divide both sides by \(5\).
\[\frac{80}{5}={u}^{2}\]

11
Simplify  \(\frac{80}{5}\)  to  \(16\).
\[16={u}^{2}\]

12
Take the square root of both sides.
\[\pm \sqrt{16}=u\]

13
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[\pm 4=u\]

14
Switch sides.
\[u=\pm 4\]

Done
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