# 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 $$5$$.$p=\pm 5$Donep=5,-5