Problem of the Week

Updated at Oct 13, 2025 12:45 PM

This week's problem comes from the equation category.

How can we solve the equation \(6{(q-3)}^{2}+4=10\)?

Let's begin!



\[6{(q-3)}^{2}+4=10\]

1
Subtract \(4\) from both sides.
\[6{(q-3)}^{2}=10-4\]

2
Simplify  \(10-4\)  to  \(6\).
\[6{(q-3)}^{2}=6\]

3
Divide both sides by \(6\).
\[{(q-3)}^{2}=1\]

4
Take the square root of both sides.
\[q-3=\pm \sqrt{1}\]

5
Simplify  \(\sqrt{1}\)  to  \(1\).
\[q-3=\pm 1\]

6
Break down the problem into these 2 equations.
\[q-3=1\]
\[q-3=-1\]

7
Solve the 1st equation: \(q-3=1\).
\[q=4\]

8
Solve the 2nd equation: \(q-3=-1\).
\[q=2\]

9
Collect all solutions.
\[q=4,2\]

Done
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