Problem of the Week

Updated at Nov 17, 2025 2:39 PM

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

How can we solve the equation \(4-5\times \frac{5}{{z}^{2}}=\frac{39}{16}\)?

Check out the solution below!



\[4-5\times \frac{5}{{z}^{2}}=\frac{39}{16}\]

1
Simplify  \(5\times \frac{5}{{z}^{2}}\)  to  \(\frac{25}{{z}^{2}}\).
\[4-\frac{25}{{z}^{2}}=\frac{39}{16}\]

2
Subtract \(4\) from both sides.
\[-\frac{25}{{z}^{2}}=\frac{39}{16}-4\]

3
Simplify  \(\frac{39}{16}-4\)  to  \(-\frac{25}{16}\).
\[-\frac{25}{{z}^{2}}=-\frac{25}{16}\]

4
Multiply both sides by \({z}^{2}\).
\[-25=-\frac{25}{16}{z}^{2}\]

5
Simplify  \(\frac{25}{16}{z}^{2}\)  to  \(\frac{25{z}^{2}}{16}\).
\[-25=-\frac{25{z}^{2}}{16}\]

6
Multiply both sides by \(16\).
\[-25\times 16=-25{z}^{2}\]

7
Simplify  \(-25\times 16\)  to  \(-400\).
\[-400=-25{z}^{2}\]

8
Divide both sides by \(-25\).
\[\frac{-400}{-25}={z}^{2}\]

9
Two negatives make a positive.
\[\frac{400}{25}={z}^{2}\]

10
Simplify  \(\frac{400}{25}\)  to  \(16\).
\[16={z}^{2}\]

11
Take the square root of both sides.
\[\pm \sqrt{16}=z\]

12
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[\pm 4=z\]

13
Switch sides.
\[z=\pm 4\]

Done
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