Problem of the Week

Updated at Apr 25, 2022 4:49 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation \({(2+q)}^{2}\times \frac{5}{4q}=\frac{45}{4}\)?

Check out the solution below!



\[{(2+q)}^{2}\times \frac{5}{4q}=\frac{45}{4}\]

1
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{{(2+q)}^{2}\times 5}{4q}=\frac{45}{4}\]

2
Regroup terms.
\[\frac{5{(2+q)}^{2}}{4q}=\frac{45}{4}\]

3
Multiply both sides by \(4q\).
\[5{(2+q)}^{2}=\frac{45}{4}\times 4q\]

4
Cancel \(4\).
\[5{(2+q)}^{2}=45q\]

5
Divide both sides by \(5\).
\[{(2+q)}^{2}=9q\]

6
Expand.
\[4+4q+{q}^{2}=9q\]

7
Move all terms to one side.
\[4+4q+{q}^{2}-9q=0\]

8
Simplify  \(4+4q+{q}^{2}-9q\)  to  \(4-5q+{q}^{2}\).
\[4-5q+{q}^{2}=0\]

9
Factor \(4-5q+{q}^{2}\).
\[(q-4)(q-1)=0\]

10
Solve for \(q\).
\[q=4,1\]

Done
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