Jen Markham

2 2 2 2 ...

2n n

2 2 ...2 2

Let’s call everything that comes after the first 2, “n”, (why can we do that??) so we can rewrite the expression as:

If n=

2 2n n

To solve for n, square both sides.

222n n

2 2 0n n Factorable???

21 ( 1) 4( 2)

2n

2 4

2

b b acn

a

Using the quadratic formula…

This then simplifies to:

1 9

2n

1 3

2n

1 3 42

2 2n

However, n=-1 is an extraneous root because if we check it in our original equation, n=-1 doesn’t

check!The final answer is n=2.

Splitting the two roots apart yields,

or1 3 2

12 2

n

The final answer is

n=2.