Problem of the Week

Updated at Nov 19, 2018 1:37 PM

How would you solve the equation \(\frac{{(4u)}^{2}}{5}+2=\frac{74}{5}\)?

Below is the solution.



\[\frac{{(4u)}^{2}}{5}+2=\frac{74}{5}\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{4}^{2}{u}^{2}}{5}+2=\frac{74}{5}\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[\frac{16{u}^{2}}{5}+2=\frac{74}{5}\]

3
Subtract \(2\) from both sides.
\[\frac{16{u}^{2}}{5}=\frac{74}{5}-2\]

4
Simplify  \(\frac{74}{5}-2\)  to  \(\frac{64}{5}\).
\[\frac{16{u}^{2}}{5}=\frac{64}{5}\]

5
Multiply both sides by \(5\).
\[16{u}^{2}=\frac{64}{5}\times 5\]

6
Cancel \(5\).
\[16{u}^{2}=64\]

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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