Problem of the Week

Updated at Dec 8, 2025 1:52 PM

How would you solve the equation \(\frac{{(4u)}^{2}-3}{5}=\frac{61}{5}\)?

Below is the solution.



\[\frac{{(4u)}^{2}-3}{5}=\frac{61}{5}\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{4}^{2}{u}^{2}-3}{5}=\frac{61}{5}\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[\frac{16{u}^{2}-3}{5}=\frac{61}{5}\]

3
Multiply both sides by \(5\).
\[16{u}^{2}-3=\frac{61}{5}\times 5\]

4
Cancel \(5\).
\[16{u}^{2}-3=61\]

5
Add \(3\) to both sides.
\[16{u}^{2}=61+3\]

6
Simplify  \(61+3\)  to  \(64\).
\[16{u}^{2}=64\]

7
Divide both sides by \(16\).
\[{u}^{2}=\frac{64}{16}\]

8
Simplify  \(\frac{64}{16}\)  to  \(4\).
\[{u}^{2}=4\]

9
Take the square root of both sides.
\[u=\pm \sqrt{4}\]

10
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[u=\pm 2\]

Done
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