Problem of the Week

Updated at Oct 5, 2026 2:39 PM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation \(6+{(2+4t)}^{2}=42\)?

Check out the solution below!



\[6+{(2+4t)}^{2}=42\]

1
Factor out the common term \(2\).
\[6+{(2(1+2t))}^{2}=42\]

2
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[6+{2}^{2}{(1+2t)}^{2}=42\]

3
Simplify  \({2}^{2}\)  to  \(4\).
\[6+4{(1+2t)}^{2}=42\]

4
Subtract \(6\) from both sides.
\[4{(1+2t)}^{2}=42-6\]

5
Simplify  \(42-6\)  to  \(36\).
\[4{(1+2t)}^{2}=36\]

6
Divide both sides by \(4\).
\[{(1+2t)}^{2}=\frac{36}{4}\]

7
Simplify  \(\frac{36}{4}\)  to  \(9\).
\[{(1+2t)}^{2}=9\]

8
Take the square root of both sides.
\[1+2t=\pm \sqrt{9}\]

9
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[1+2t=\pm 3\]

10
Break down the problem into these 2 equations.
\[1+2t=3\]
\[1+2t=-3\]

11
Solve the 1st equation: \(1+2t=3\).
\[t=1\]

12
Solve the 2nd equation: \(1+2t=-3\).
\[t=-2\]

13
Collect all solutions.
\[t=1,-2\]

Done
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