# 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 $${x}^{2}+2x-35$$.1 Ask: Which two numbers add up to $$2$$ and multiply to $$-35$$?$$-5$$ and $$7$$2 Rewrite the expression using the above.$(x-5)(x+7)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$(x-5)(x+7)=0$11 Solve for $$x$$.1 Ask: When will $$(x-5)(x+7)$$ equal zero?When $$x-5=0$$ or $$x+7=0$$2 Solve each of the 2 equations above.$x=5,-7$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$x=5,-7$Donex=5,-7