Problem of the Week

Updated at Nov 10, 2025 11:56 AM

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

How would you solve \(\frac{{(y+2)}^{2}-3}{2}=\frac{33}{2}\)?

Here are the steps:



\[\frac{{(y+2)}^{2}-3}{2}=\frac{33}{2}\]

1
Multiply both sides by \(2\).
\[{(y+2)}^{2}-3=\frac{33}{2}\times 2\]

2
Cancel \(2\).
\[{(y+2)}^{2}-3=33\]

3
Add \(3\) to both sides.
\[{(y+2)}^{2}=33+3\]

4
Simplify  \(33+3\)  to  \(36\).
\[{(y+2)}^{2}=36\]

5
Take the square root of both sides.
\[y+2=\pm \sqrt{36}\]

6
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[y+2=\pm 6\]

7
Break down the problem into these 2 equations.
\[y+2=6\]
\[y+2=-6\]

8
Solve the 1st equation: \(y+2=6\).
\[y=4\]

9
Solve the 2nd equation: \(y+2=-6\).
\[y=-8\]

10
Collect all solutions.
\[y=4,-8\]

Done
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