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
Simplify \(\frac{64}{5}\times 5\) to \(\frac{320}{5}\).
\[16{u}^{2}=\frac{320}{5}\]

7
Simplify \(\frac{320}{5}\) to \(64\).
\[16{u}^{2}=64\]

8
Divide both sides by \(16\).
\[{u}^{2}=\frac{64}{16}\]

9
Simplify \(\frac{64}{16}\) to \(4\).
\[{u}^{2}=4\]

10
Take the square root of both sides.
\[u=\pm \sqrt{4}\]

11
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[u=\pm 2\]

Done