# Problem of the Week

## Updated at Sep 6, 2021 5:25 PM

This week's problem comes from the equation category.

How would you solve the equation $$\frac{{(v+2)}^{2}-6}{3}=1$$?

Let's begin!

$\frac{{(v+2)}^{2}-6}{3}=1$

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