Problem of the Week

Updated at Mar 16, 2026 1:16 PM

For this week we've brought you this equation problem.

How would you solve the equation \(\frac{4}{2}(t-3)(t-3)=8\)?

Here are the steps:



\[\frac{4}{2}(t-3)(t-3)=8\]

1
Simplify  \(\frac{4}{2}\)  to  \(2\).
\[2(t-3)(t-3)=8\]

2
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[2{(t-3)}^{2}=8\]

3
Divide both sides by \(2\).
\[{(t-3)}^{2}=\frac{8}{2}\]

4
Simplify  \(\frac{8}{2}\)  to  \(4\).
\[{(t-3)}^{2}=4\]

5
Take the square root of both sides.
\[t-3=\pm \sqrt{4}\]

6
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[t-3=\pm 2\]

7
Break down the problem into these 2 equations.
\[t-3=2\]
\[t-3=-2\]

8
Solve the 1st equation: \(t-3=2\).
\[t=5\]

9
Solve the 2nd equation: \(t-3=-2\).
\[t=1\]

10
Collect all solutions.
\[t=5,1\]

Done
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