Problem of the Week

Updated at Dec 11, 2023 1:20 PM

This week's problem comes from the equation category.

How would you solve \({(\frac{4}{5}m-3)}^{2}=\frac{1}{25}\)?

Let's begin!



\[{(\frac{4}{5}m-3)}^{2}=\frac{1}{25}\]

1
Simplify  \(\frac{4}{5}m\)  to  \(\frac{4m}{5}\).
\[{(\frac{4m}{5}-3)}^{2}=\frac{1}{25}\]

2
Take the square root of both sides.
\[\frac{4m}{5}-3=\pm \sqrt{\frac{1}{25}}\]

3
Simplify  \(\sqrt{\frac{1}{25}}\)  to  \(\frac{\sqrt{1}}{\sqrt{25}}\).
\[\frac{4m}{5}-3=\pm \frac{\sqrt{1}}{\sqrt{25}}\]

4
Simplify  \(\sqrt{1}\)  to  \(1\).
\[\frac{4m}{5}-3=\pm \frac{1}{\sqrt{25}}\]

5
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[\frac{4m}{5}-3=\pm \frac{1}{5}\]

6
Break down the problem into these 2 equations.
\[\frac{4m}{5}-3=\frac{1}{5}\]
\[\frac{4m}{5}-3=-\frac{1}{5}\]

7
Solve the 1st equation: \(\frac{4m}{5}-3=\frac{1}{5}\).
\[m=4\]

8
Solve the 2nd equation: \(\frac{4m}{5}-3=-\frac{1}{5}\).
\[m=\frac{7}{2}\]

9
Collect all solutions.
\[m=4,\frac{7}{2}\]

Done

Decimal Form: 4, 3.5
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