Problem of the Week

Updated at May 9, 2022 5:21 PM

For this week we've brought you this equation problem.

How can we solve the equation \(\frac{50}{x(2+x)}=\frac{10}{7}\)?

Here are the steps:



\[\frac{50}{x(2+x)}=\frac{10}{7}\]

1
Multiply both sides by \(x(2+x)\).
\[50=\frac{10}{7}x(2+x)\]

2
Simplify  \(\frac{10}{7}x(2+x)\)  to  \(\frac{10x(2+x)}{7}\).
\[50=\frac{10x(2+x)}{7}\]

3
Multiply both sides by \(7\).
\[350=10x(2+x)\]

4
Expand.
\[350=20x+10{x}^{2}\]

5
Move all terms to one side.
\[350-20x-10{x}^{2}=0\]

6
Factor out the common term \(10\).
\[10(35-2x-{x}^{2})=0\]

7
Factor out the negative sign.
\[10\times -({x}^{2}+2x-35)=0\]

8
Divide both sides by \(10\).
\[-{x}^{2}-2x+35=0\]

9
Multiply both sides by \(-1\).
\[{x}^{2}+2x-35=0\]

10
Factor \({x}^{2}+2x-35\).
\[(x-5)(x+7)=0\]

11
Solve for \(x\).
\[x=5,-7\]

Done
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