Problem of the Week

Updated at Sep 1, 2025 5:19 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation \(3-4{(\frac{5}{m})}^{2}=-\frac{73}{9}\)?

Check out the solution below!



\[3-4{(\frac{5}{m})}^{2}=-\frac{73}{9}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[3-4\times \frac{{5}^{2}}{{m}^{2}}=-\frac{73}{9}\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[3-4\times \frac{25}{{m}^{2}}=-\frac{73}{9}\]

3
Simplify  \(4\times \frac{25}{{m}^{2}}\)  to  \(\frac{100}{{m}^{2}}\).
\[3-\frac{100}{{m}^{2}}=-\frac{73}{9}\]

4
Subtract \(3\) from both sides.
\[-\frac{100}{{m}^{2}}=-\frac{73}{9}-3\]

5
Simplify  \(-\frac{73}{9}-3\)  to  \(-\frac{100}{9}\).
\[-\frac{100}{{m}^{2}}=-\frac{100}{9}\]

6
Multiply both sides by \({m}^{2}\).
\[-100=-\frac{100}{9}{m}^{2}\]

7
Simplify  \(\frac{100}{9}{m}^{2}\)  to  \(\frac{100{m}^{2}}{9}\).
\[-100=-\frac{100{m}^{2}}{9}\]

8
Multiply both sides by \(9\).
\[-100\times 9=-100{m}^{2}\]

9
Simplify  \(-100\times 9\)  to  \(-900\).
\[-900=-100{m}^{2}\]

10
Divide both sides by \(-100\).
\[\frac{-900}{-100}={m}^{2}\]

11
Two negatives make a positive.
\[\frac{900}{100}={m}^{2}\]

12
Simplify  \(\frac{900}{100}\)  to  \(9\).
\[9={m}^{2}\]

13
Take the square root of both sides.
\[\pm \sqrt{9}=m\]

14
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[\pm 3=m\]

15
Switch sides.
\[m=\pm 3\]

Done
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