Problem of the Week

Updated at Mar 4, 2019 1:58 PM

This week we have another equation problem:

How would you solve the equation \(6{(\frac{5}{2+w})}^{2}=\frac{25}{6}\)?

Let's start!



\[6{(\frac{5}{2+w})}^{2}=\frac{25}{6}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[6\times \frac{{5}^{2}}{{(2+w)}^{2}}=\frac{25}{6}\]

2
Simplify \({5}^{2}\) to \(25\).
\[6\times \frac{25}{{(2+w)}^{2}}=\frac{25}{6}\]

3
Simplify \(6\times \frac{25}{{(2+w)}^{2}}\) to \(\frac{150}{{(2+w)}^{2}}\).
\[\frac{150}{{(2+w)}^{2}}=\frac{25}{6}\]

4
Multiply both sides by \({(2+w)}^{2}\).
\[150=\frac{25}{6}{(2+w)}^{2}\]

5
Simplify \(\frac{25}{6}{(2+w)}^{2}\) to \(\frac{25{(2+w)}^{2}}{6}\).
\[150=\frac{25{(2+w)}^{2}}{6}\]

6
Multiply both sides by \(6\).
\[150\times 6=25{(2+w)}^{2}\]

7
Simplify \(150\times 6\) to \(900\).
\[900=25{(2+w)}^{2}\]

8
Divide both sides by \(25\).
\[\frac{900}{25}={(2+w)}^{2}\]

9
Simplify \(\frac{900}{25}\) to \(36\).
\[36={(2+w)}^{2}\]

10
Take the square root of both sides.
\[\pm \sqrt{36}=2+w\]

11
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[\pm 6=2+w\]

12
Switch sides.
\[2+w=\pm 6\]

13
Break down the problem into these 2 equations.
\[2+w=6\]
\[2+w=-6\]

14
How?
Solve the 1st equation: \(2+w=6\).
\[w=4\]

15
How?
Solve the 2nd equation: \(2+w=-6\).
\[w=-8\]

16
Collect all solutions.
\[w=4,-8\]

Done