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 50x(2+x)=107\frac{50}{x(2+x)}=\frac{10}{7}?

Here are the steps:



50x(2+x)=107\frac{50}{x(2+x)}=\frac{10}{7}

1
Multiply both sides by x(2+x)x(2+x).
50=107x(2+x)50=\frac{10}{7}x(2+x)

2
Simplify  107x(2+x)\frac{10}{7}x(2+x)  to  10x(2+x)7\frac{10x(2+x)}{7}.
50=10x(2+x)750=\frac{10x(2+x)}{7}

3
Multiply both sides by 77.
350=10x(2+x)350=10x(2+x)

4
Expand.
350=20x+10x2350=20x+10{x}^{2}

5
Move all terms to one side.
350−20x−10x2=0350-20x-10{x}^{2}=0

6
Factor out the common term 1010.
10(35−2x−x2)=010(35-2x-{x}^{2})=0

7
Factor out the negative sign.
10×−(x2+2x−35)=010\times -({x}^{2}+2x-35)=0

8
Divide both sides by 1010.
−x2−2x+35=0-{x}^{2}-2x+35=0

9
Multiply both sides by −1-1.
x2+2x−35=0{x}^{2}+2x-35=0

10
Factor x2+2x−35{x}^{2}+2x-35.
(x−5)(x+7)=0(x-5)(x+7)=0

11
Solve for xx.
x=5,−7x=5,-7

Done
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