Problem of the Week

Updated at Mar 25, 2019 1:05 PM

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Mar 25, 2019

This week's problem comes from the equation category.

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

Let's begin!

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

Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).

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

Simplify \({5}^{2}\) to \(25\).

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

Divide both sides by \(2\).

\[\frac{{p}^{2}}{25}+6=\frac{14}{2}\]

Simplify \(\frac{14}{2}\) to \(7\).

\[\frac{{p}^{2}}{25}+6=7\]

Subtract \(6\) from both sides.

\[\frac{{p}^{2}}{25}=7-6\]

Simplify \(7-6\) to \(1\).

\[\frac{{p}^{2}}{25}=1\]

Multiply both sides by \(25\).

\[{p}^{2}=1\times 25\]

Simplify \(1\times 25\) to \(25\).

\[{p}^{2}=25\]

Take the square root of both sides.

\[p=\pm \sqrt{25}\]

Since \(5\times 5=25\), the square root of \(25\) is \(5\).

\[p=\pm 5\]

Done