Problem of the Week

Updated at May 25, 2026 5:15 PM

This week's problem comes from the equation category.

How can we solve the equation \({({u}^{2}-6)}^{2}-3=22\)?

Let's begin!



\[{({u}^{2}-6)}^{2}-3=22\]

1
Add \(3\) to both sides.
\[{({u}^{2}-6)}^{2}=22+3\]

2
Simplify  \(22+3\)  to  \(25\).
\[{({u}^{2}-6)}^{2}=25\]

3
Take the square root of both sides.
\[{u}^{2}-6=\pm \sqrt{25}\]

4
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[{u}^{2}-6=\pm 5\]

5
Break down the problem into these 2 equations.
\[{u}^{2}-6=5\]
\[{u}^{2}-6=-5\]

6
Solve the 1st equation: \({u}^{2}-6=5\).
\[u=\pm \sqrt{11}\]

7
Solve the 2nd equation: \({u}^{2}-6=-5\).
\[u=\pm 1\]

8
Collect all solutions.
\[u=\pm \sqrt{11},\pm 1\]

Done

Decimal Form: ±3.316625, ±1
Cymath foriOSAndroid