Problem of the Week

Updated at Apr 14, 2025 5:50 PM

This week's problem comes from the equation category.

How would you solve \(\frac{2(3-{t}^{2})}{3-t}=26\)?

Let's begin!



\[\frac{2(3-{t}^{2})}{3-t}=26\]

1
Multiply both sides by \(3-t\).
\[2(3-{t}^{2})=26(3-t)\]

2
Divide both sides by \(2\).
\[3-{t}^{2}=13(3-t)\]

3
Expand.
\[3-{t}^{2}=39-13t\]

4
Move all terms to one side.
\[3-{t}^{2}-39+13t=0\]

5
Simplify  \(3-{t}^{2}-39+13t\)  to  \(-36-{t}^{2}+13t\).
\[-36-{t}^{2}+13t=0\]

6
Multiply both sides by \(-1\).
\[{t}^{2}-13t+36=0\]

7
Factor \({t}^{2}-13t+36\).
\[(t-9)(t-4)=0\]

8
Solve for \(t\).
\[t=9,4\]

Done
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