Problem of the Week

Updated at Aug 10, 2026 2:52 PM

How would you solve the equation \({({(m-3)}^{2}+6)}^{2}=36\)?

Below is the solution.



\[{({(m-3)}^{2}+6)}^{2}=36\]

1
Take the square root of both sides.
\[{(m-3)}^{2}+6=\pm \sqrt{36}\]

2
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[{(m-3)}^{2}+6=\pm 6\]

3
Break down the problem into these 2 equations.
\[{(m-3)}^{2}+6=6\]
\[{(m-3)}^{2}+6=-6\]

4
Solve the 1st equation: \({(m-3)}^{2}+6=6\).
\[m=3\]

5
Solve the 2nd equation: \({(m-3)}^{2}+6=-6\).
\[m=3+2\sqrt{3}\imath ,3-2\sqrt{3}\imath \]

6
Collect all solutions.
\[m=3,3+2\sqrt{3}\imath ,3-2\sqrt{3}\imath \]

Done
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