Problem of the Week

Updated at Jun 8, 2020 11:44 AM

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

How would you solve \(6-{(3-\frac{5}{u})}^{2}=2\)?

Check out the solution below!



\[6-{(3-\frac{5}{u})}^{2}=2\]

1
Subtract \(6\) from both sides.
\[-{(3-\frac{5}{u})}^{2}=2-6\]

2
Simplify  \(2-6\)  to  \(-4\).
\[-{(3-\frac{5}{u})}^{2}=-4\]

3
Multiply both sides by \(-1\).
\[{(3-\frac{5}{u})}^{2}=4\]

4
Take the square root of both sides.
\[3-\frac{5}{u}=\pm \sqrt{4}\]

5
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[3-\frac{5}{u}=\pm 2\]

6
Break down the problem into these 2 equations.
\[3-\frac{5}{u}=2\]
\[3-\frac{5}{u}=-2\]

7
Solve the 1st equation: \(3-\frac{5}{u}=2\).
\[u=5\]

8
Solve the 2nd equation: \(3-\frac{5}{u}=-2\).
\[u=1\]

9
Collect all solutions.
\[u=5,1\]

Done
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