Problem of the Week

Updated at Feb 28, 2022 12:38 PM

This week we have another equation problem:

How would you solve \(\frac{{(\frac{u+2}{2})}^{2}}{5}=\frac{9}{5}\)?

Let's start!



\[\frac{{(\frac{u+2}{2})}^{2}}{5}=\frac{9}{5}\]

1
Simplify  \(\frac{u+2}{2}\)  to  \(1+\frac{u}{2}\).
\[\frac{{(1+\frac{u}{2})}^{2}}{5}=\frac{9}{5}\]

2
Multiply both sides by \(5\).
\[{(1+\frac{u}{2})}^{2}=\frac{9}{5}\times 5\]

3
Cancel \(5\).
\[{(1+\frac{u}{2})}^{2}=9\]

4
Take the square root of both sides.
\[1+\frac{u}{2}=\pm \sqrt{9}\]

5
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[1+\frac{u}{2}=\pm 3\]

6
Break down the problem into these 2 equations.
\[1+\frac{u}{2}=3\]
\[1+\frac{u}{2}=-3\]

7
Solve the 1st equation: \(1+\frac{u}{2}=3\).
\[u=4\]

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

9
Collect all solutions.
\[u=4,-8\]

Done
Cymath foriOSAndroid