Problem of the Week

Updated at Mar 28, 2022 4:33 PM

This week we have another equation problem:

How can we solve the equation \(\frac{3}{6-{(3-z)}^{2}}=\frac{1}{2}\)?

Let's start!



\[\frac{3}{6-{(3-z)}^{2}}=\frac{1}{2}\]

1
Multiply both sides by \(6-{(3-z)}^{2}\).
\[3=\frac{1}{2}(6-{(3-z)}^{2})\]

2
Simplify  \(\frac{1}{2}(6-{(3-z)}^{2})\)  to  \(\frac{6-{(3-z)}^{2}}{2}\).
\[3=\frac{6-{(3-z)}^{2}}{2}\]

3
Multiply both sides by \(2\).
\[3\times 2=6-{(3-z)}^{2}\]

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

5
Cancel \(6\) on both sides.
\[0=-{(3-z)}^{2}\]

6
Multiply both sides by \(-1\).
\[0={(3-z)}^{2}\]

7
Take the square root of both sides.
\[0=3-z\]

8
Subtract \(3\) from both sides.
\[-3=-z\]

9
Multiply both sides by \(-1\).
\[3=z\]

10
Switch sides.
\[z=3\]

Done
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