Problem of the Week

Updated at Apr 21, 2025 4:43 PM

This week we have another equation problem:

How would you solve the equation 5p(p+2)25=245\frac{5p(p+2)}{25}=\frac{24}{5}?

Let's start!



5p(p+2)25=245\frac{5p(p+2)}{25}=\frac{24}{5}

1
Simplify  5p(p+2)25\frac{5p(p+2)}{25}  to  p(p+2)5\frac{p(p+2)}{5}.
p(p+2)5=245\frac{p(p+2)}{5}=\frac{24}{5}

2
Multiply both sides by 55.
p(p+2)=24p(p+2)=24

3
Expand.
p2+2p=24{p}^{2}+2p=24

4
Move all terms to one side.
p2+2p−24=0{p}^{2}+2p-24=0

5
Factor p2+2p−24{p}^{2}+2p-24.
(p−4)(p+6)=0(p-4)(p+6)=0

6
Solve for pp.
p=4,−6p=4,-6

Done
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