Problem of the Week

Updated at May 27, 2024 12:45 PM

This week's problem comes from the equation category.

How can we solve the equation (n−3)(n+2)25=1425\frac{(n-3)(n+2)}{25}=\frac{14}{25}?

Let's begin!



(n−3)(n+2)25=1425\frac{(n-3)(n+2)}{25}=\frac{14}{25}

1
Multiply both sides by 2525.
(n−3)(n+2)=14(n-3)(n+2)=14

2
Expand.
n2+2n−3n−6=14{n}^{2}+2n-3n-6=14

3
Simplify  n2+2n−3n−6{n}^{2}+2n-3n-6  to  n2−n−6{n}^{2}-n-6.
n2−n−6=14{n}^{2}-n-6=14

4
Move all terms to one side.
n2−n−6−14=0{n}^{2}-n-6-14=0

5
Simplify  n2−n−6−14{n}^{2}-n-6-14  to  n2−n−20{n}^{2}-n-20.
n2−n−20=0{n}^{2}-n-20=0

6
Factor n2−n−20{n}^{2}-n-20.
(n−5)(n+4)=0(n-5)(n+4)=0

7
Solve for nn.
n=5,−4n=5,-4

Done
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