Problem of the Week

Updated at Dec 9, 2019 2:25 PM

This week's problem comes from the equation category.

How would you solve the equation \({(4\times \frac{5}{2+w})}^{2}=25\)?

Let's begin!



\[{(4\times \frac{5}{2+w})}^{2}=25\]

1
Simplify  \(4\times \frac{5}{2+w}\)  to  \(\frac{20}{2+w}\).
\[{(\frac{20}{2+w})}^{2}=25\]

2
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{{20}^{2}}{{(2+w)}^{2}}=25\]

3
Simplify  \({20}^{2}\)  to  \(400\).
\[\frac{400}{{(2+w)}^{2}}=25\]

4
Multiply both sides by \({(2+w)}^{2}\).
\[400=25{(2+w)}^{2}\]

5
Divide both sides by \(25\).
\[\frac{400}{25}={(2+w)}^{2}\]

6
Simplify  \(\frac{400}{25}\)  to  \(16\).
\[16={(2+w)}^{2}\]

7
Take the square root of both sides.
\[\pm \sqrt{16}=2+w\]

8
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[\pm 4=2+w\]

9
Switch sides.
\[2+w=\pm 4\]

10
Break down the problem into these 2 equations.
\[2+w=4\]
\[2+w=-4\]

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

12
Solve the 2nd equation: \(2+w=-4\).
\[w=-6\]

13
Collect all solutions.
\[w=2,-6\]

Done
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