Problem of the Week

Updated at Mar 9, 2026 10:25 AM

This week's problem comes from the equation category.

How would you solve the equation \(\frac{{m}^{2}}{5}\times \frac{m+2}{5}=\frac{3}{25}\)?

Let's begin!



\[\frac{{m}^{2}}{5}\times \frac{m+2}{5}=\frac{3}{25}\]

1
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{{m}^{2}(m+2)}{5\times 5}=\frac{3}{25}\]

2
Simplify  \(5\times 5\)  to  \(25\).
\[\frac{{m}^{2}(m+2)}{25}=\frac{3}{25}\]

3
Multiply both sides by \(25\).
\[{m}^{2}(m+2)=3\]

4
Expand.
\[{m}^{3}+2{m}^{2}=3\]

5
Move all terms to one side.
\[{m}^{3}+2{m}^{2}-3=0\]

6
Factor \({m}^{3}+2{m}^{2}-3\) using Polynomial Division.
\[({m}^{2}+3m+3)(m-1)=0\]

7
Solve for \(m\).
\[m=1\]

8
Use the Quadratic Formula.
\[m=\frac{-3+\sqrt{3}\imath }{2},\frac{-3-\sqrt{3}\imath }{2}\]

9
Collect all solutions from the previous steps.
\[m=1,\frac{-3+\sqrt{3}\imath }{2},\frac{-3-\sqrt{3}\imath }{2}\]

Done
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