# Problem of the Week

## Updated at Aug 1, 2022 12:33 PM

This week we have another equation problem:

How can we solve the equation $${(\frac{n}{5}-3)}^{2}-3=1$$?

Let's start!

${(\frac{n}{5}-3)}^{2}-3=1$

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