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((p5)2+6)=142({(\frac{p}{5})}^{2}+6)=14?

Let's begin!



2((p5)2+6)=142({(\frac{p}{5})}^{2}+6)=14

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
2(p252+6)=142(\frac{{p}^{2}}{{5}^{2}}+6)=14

2
Simplify  52{5}^{2}  to  2525.
2(p225+6)=142(\frac{{p}^{2}}{25}+6)=14

3
Divide both sides by 22.
p225+6=142\frac{{p}^{2}}{25}+6=\frac{14}{2}

4
Simplify  142\frac{14}{2}  to  77.
p225+6=7\frac{{p}^{2}}{25}+6=7

5
Subtract 66 from both sides.
p225=7−6\frac{{p}^{2}}{25}=7-6

6
Simplify  7−67-6  to  11.
p225=1\frac{{p}^{2}}{25}=1

7
Multiply both sides by 2525.
p2=1×25{p}^{2}=1\times 25

8
Simplify  1×251\times 25  to  2525.
p2=25{p}^{2}=25

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

10
Since 5×5=255\times 5=25, the square root of 2525 is 55.
p=±5p=\pm 5

Done
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