Problem of the Week

Updated at Mar 25, 2019 1:05 PM

This week's problem comes from the equation category.

How would you solve \(2({(\frac{p}{5})}^{2}+6)=14\)?

Let's begin!



\[2({(\frac{p}{5})}^{2}+6)=14\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[2(\frac{{p}^{2}}{{5}^{2}}+6)=14\]

2
Simplify \({5}^{2}\) to \(25\).
\[2(\frac{{p}^{2}}{25}+6)=14\]

3
Divide both sides by \(2\).
\[\frac{{p}^{2}}{25}+6=\frac{14}{2}\]

4
Simplify \(\frac{14}{2}\) to \(7\).
\[\frac{{p}^{2}}{25}+6=7\]

5
Subtract \(6\) from both sides.
\[\frac{{p}^{2}}{25}=7-6\]

6
Simplify \(7-6\) to \(1\).
\[\frac{{p}^{2}}{25}=1\]

7
Multiply both sides by \(25\).
\[{p}^{2}=1\times 25\]

8
Simplify \(1\times 25\) to \(25\).
\[{p}^{2}=25\]

9
Take the square root of both sides.
\[p=\pm \sqrt{25}\]

10
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[p=\pm 5\]

Done