Problem of the Week

Updated at May 15, 2023 11:28 AM

This week we have another equation problem:

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

Let's start!



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

1
Take the square root of both sides.
\[\frac{w+2}{5}+2=\pm \sqrt{9}\]

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

3
Break down the problem into these 2 equations.
\[\frac{w+2}{5}+2=3\]
\[\frac{w+2}{5}+2=-3\]

4
Solve the 1st equation: \(\frac{w+2}{5}+2=3\).
\[w=3\]

5
Solve the 2nd equation: \(\frac{w+2}{5}+2=-3\).
\[w=-27\]

6
Collect all solutions.
\[w=3,-27\]

Done
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