Problem of the Week

Updated at Jan 24, 2022 8:49 AM

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

How would you solve the equation \(4\times \frac{5}{{(2+t)}^{2}}=\frac{20}{49}\)?

Check out the solution below!



\[4\times \frac{5}{{(2+t)}^{2}}=\frac{20}{49}\]

1
Simplify  \(4\times \frac{5}{{(2+t)}^{2}}\)  to  \(\frac{20}{{(2+t)}^{2}}\).
\[\frac{20}{{(2+t)}^{2}}=\frac{20}{49}\]

2
Multiply both sides by \({(2+t)}^{2}\).
\[20=\frac{20}{49}{(2+t)}^{2}\]

3
Simplify  \(\frac{20}{49}{(2+t)}^{2}\)  to  \(\frac{20{(2+t)}^{2}}{49}\).
\[20=\frac{20{(2+t)}^{2}}{49}\]

4
Multiply both sides by \(49\).
\[20\times 49=20{(2+t)}^{2}\]

5
Simplify  \(20\times 49\)  to  \(980\).
\[980=20{(2+t)}^{2}\]

6
Divide both sides by \(20\).
\[\frac{980}{20}={(2+t)}^{2}\]

7
Simplify  \(\frac{980}{20}\)  to  \(49\).
\[49={(2+t)}^{2}\]

8
Take the square root of both sides.
\[\pm \sqrt{49}=2+t\]

9
Since \(7\times 7=49\), the square root of \(49\) is \(7\).
\[\pm 7=2+t\]

10
Switch sides.
\[2+t=\pm 7\]

11
Break down the problem into these 2 equations.
\[2+t=7\]
\[2+t=-7\]

12
Solve the 1st equation: \(2+t=7\).
\[t=5\]

13
Solve the 2nd equation: \(2+t=-7\).
\[t=-9\]

14
Collect all solutions.
\[t=5,-9\]

Done
Cymath foriOSAndroid