# Problem of the Week

## Updated at Feb 28, 2022 12:38 PM

This week we have another equation problem:

How would you solve $$\frac{{(\frac{u+2}{2})}^{2}}{5}=\frac{9}{5}$$?

Let's start!

$\frac{{(\frac{u+2}{2})}^{2}}{5}=\frac{9}{5}$

 1 Simplify  $$\frac{u+2}{2}$$  to  $$1+\frac{u}{2}$$.$\frac{{(1+\frac{u}{2})}^{2}}{5}=\frac{9}{5}$2 Multiply both sides by $$5$$.${(1+\frac{u}{2})}^{2}=\frac{9}{5}\times 5$3 Cancel $$5$$.${(1+\frac{u}{2})}^{2}=9$4 Take the square root of both sides.$1+\frac{u}{2}=\pm \sqrt{9}$5 Since $$3\times 3=9$$, the square root of $$9$$ is $$3$$.$1+\frac{u}{2}=\pm 3$6 Break down the problem into these 2 equations.$1+\frac{u}{2}=3$$1+\frac{u}{2}=-3$7 Solve the 1st equation: $$1+\frac{u}{2}=3$$.1 Subtract $$1$$ from both sides.$\frac{u}{2}=3-1$2 Simplify  $$3-1$$  to  $$2$$.$\frac{u}{2}=2$3 Multiply both sides by $$2$$.$u=2\times 2$4 Simplify  $$2\times 2$$  to  $$4$$.$u=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=4$8 Solve the 2nd equation: $$1+\frac{u}{2}=-3$$.1 Subtract $$1$$ from both sides.$\frac{u}{2}=-3-1$2 Simplify  $$-3-1$$  to  $$-4$$.$\frac{u}{2}=-4$3 Multiply both sides by $$2$$.$u=-4\times 2$4 Simplify  $$4\times 2$$  to  $$8$$.$u=-8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=-8$9 Collect all solutions.$u=4,-8$Doneu=4,-8