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 (v+2)2−63=1\frac{{(v+2)}^{2}-6}{3}=1?

Let's begin!



(v+2)2−63=1\frac{{(v+2)}^{2}-6}{3}=1

1
Multiply both sides by 33.
(v+2)2−6=1×3{(v+2)}^{2}-6=1\times 3

2
Simplify  1×31\times 3  to  33.
(v+2)2−6=3{(v+2)}^{2}-6=3

3
Add 66 to both sides.
(v+2)2=3+6{(v+2)}^{2}=3+6

4
Simplify  3+63+6  to  99.
(v+2)2=9{(v+2)}^{2}=9

5
Take the square root of both sides.
v+2=±9v+2=\pm \sqrt{9}

6
Since 3×3=93\times 3=9, the square root of 99 is 33.
v+2=±3v+2=\pm 3

7
Break down the problem into these 2 equations.
v+2=3v+2=3
v+2=−3v+2=-3

8
Solve the 1st equation: v+2=3v+2=3.
v=1v=1

9
Solve the 2nd equation: v+2=−3v+2=-3.
v=−5v=-5

10
Collect all solutions.
v=1,−5v=1,-5

Done
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