Problem of the Week

Updated at Jul 29, 2024 1:01 PM

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

How would you solve the equation \({({x}^{2}-6)}^{2}+2=11\)?

Here are the steps:



\[{({x}^{2}-6)}^{2}+2=11\]

1
Subtract \(2\) from both sides.
\[{({x}^{2}-6)}^{2}=11-2\]

2
Simplify  \(11-2\)  to  \(9\).
\[{({x}^{2}-6)}^{2}=9\]

3
Take the square root of both sides.
\[{x}^{2}-6=\pm \sqrt{9}\]

4
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[{x}^{2}-6=\pm 3\]

5
Break down the problem into these 2 equations.
\[{x}^{2}-6=3\]
\[{x}^{2}-6=-3\]

6
Solve the 1st equation: \({x}^{2}-6=3\).
\[x=\pm 3\]

7
Solve the 2nd equation: \({x}^{2}-6=-3\).
\[x=\pm \sqrt{3}\]

8
Collect all solutions.
\[x=\pm 3,\pm \sqrt{3}\]

Done

Decimal Form: ±3, ±1.732051
Cymath foriOSAndroid