Problem of the Week

Updated at Jul 24, 2023 10:51 AM

For this week we've brought you this equation problem.

How can we solve the equation \(5+\frac{6}{{(2+w)}^{2}}=\frac{31}{6}\)?

Here are the steps:



\[5+\frac{6}{{(2+w)}^{2}}=\frac{31}{6}\]

1
Subtract \(5\) from both sides.
\[\frac{6}{{(2+w)}^{2}}=\frac{31}{6}-5\]

2
Simplify  \(\frac{31}{6}-5\)  to  \(\frac{1}{6}\).
\[\frac{6}{{(2+w)}^{2}}=\frac{1}{6}\]

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

4
Simplify  \(\frac{1}{6}{(2+w)}^{2}\)  to  \(\frac{{(2+w)}^{2}}{6}\).
\[6=\frac{{(2+w)}^{2}}{6}\]

5
Multiply both sides by \(6\).
\[6\times 6={(2+w)}^{2}\]

6
Simplify  \(6\times 6\)  to  \(36\).
\[36={(2+w)}^{2}\]

7
Take the square root of both sides.
\[\pm \sqrt{36}=2+w\]

8
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[\pm 6=2+w\]

9
Switch sides.
\[2+w=\pm 6\]

10
Break down the problem into these 2 equations.
\[2+w=6\]
\[2+w=-6\]

11
Solve the 1st equation: \(2+w=6\).
\[w=4\]

12
Solve the 2nd equation: \(2+w=-6\).
\[w=-8\]

13
Collect all solutions.
\[w=4,-8\]

Done
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