Problem of the Week

Updated at Jan 1, 2024 11:08 AM

This week we have another equation problem:

How would you solve \({({(m-3)}^{2}+6)}^{2}=49\)?

Let's start!



\[{({(m-3)}^{2}+6)}^{2}=49\]

1
Take the square root of both sides.
\[{(m-3)}^{2}+6=\pm \sqrt{49}\]

2
Since \(7\times 7=49\), the square root of \(49\) is \(7\).
\[{(m-3)}^{2}+6=\pm 7\]

3
Break down the problem into these 2 equations.
\[{(m-3)}^{2}+6=7\]
\[{(m-3)}^{2}+6=-7\]

4
Solve the 1st equation: \({(m-3)}^{2}+6=7\).
\[m=4,2\]

5
Solve the 2nd equation: \({(m-3)}^{2}+6=-7\).
\[m=3+\sqrt{13}\imath ,3-\sqrt{13}\imath \]

6
Collect all solutions.
\[m=4,2,3+\sqrt{13}\imath ,3-\sqrt{13}\imath \]

Done
Cymath foriOSAndroid