# Problem of the Week

## Updated at Oct 26, 2020 11:51 AM

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

How can we solve the equation $${(\frac{u}{5}+2)}^{2}-6=\frac{19}{25}$$?

Here are the steps:

${(\frac{u}{5}+2)}^{2}-6=\frac{19}{25}$

 1 Add $$6$$ to both sides.${(\frac{u}{5}+2)}^{2}=\frac{19}{25}+6$2 Simplify  $$\frac{19}{25}+6$$  to  $$\frac{169}{25}$$.${(\frac{u}{5}+2)}^{2}=\frac{169}{25}$3 Take the square root of both sides.$\frac{u}{5}+2=\pm \sqrt{\frac{169}{25}}$4 Simplify  $$\sqrt{\frac{169}{25}}$$  to  $$\frac{\sqrt{169}}{\sqrt{25}}$$.$\frac{u}{5}+2=\pm \frac{\sqrt{169}}{\sqrt{25}}$5 Since $$13\times 13=169$$, the square root of $$169$$ is $$13$$.$\frac{u}{5}+2=\pm \frac{13}{\sqrt{25}}$6 Since $$5\times 5=25$$, the square root of $$25$$ is $$5$$.$\frac{u}{5}+2=\pm \frac{13}{5}$7 Break down the problem into these 2 equations.$\frac{u}{5}+2=\frac{13}{5}$$\frac{u}{5}+2=-\frac{13}{5}$8 Solve the 1st equation: $$\frac{u}{5}+2=\frac{13}{5}$$.1 Subtract $$2$$ from both sides.$\frac{u}{5}=\frac{13}{5}-2$2 Simplify  $$\frac{13}{5}-2$$  to  $$\frac{3}{5}$$.$\frac{u}{5}=\frac{3}{5}$3 Multiply both sides by $$5$$.$u=\frac{3}{5}\times 5$4 Cancel $$5$$.$u=3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=3$9 Solve the 2nd equation: $$\frac{u}{5}+2=-\frac{13}{5}$$.1 Subtract $$2$$ from both sides.$\frac{u}{5}=-\frac{13}{5}-2$2 Simplify  $$-\frac{13}{5}-2$$  to  $$-\frac{23}{5}$$.$\frac{u}{5}=-\frac{23}{5}$3 Multiply both sides by $$5$$.$u=-\frac{23}{5}\times 5$4 Cancel $$5$$.$u=-23$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$u=-23$10 Collect all solutions.$u=3,-23$Doneu=3,-23