Problem Number Two

Students have had a week to work on the Magic Trick problem, and they are doing amazing thinking.  Most students have made significant progress.  To do so, they have had to consider important mathematical issues like place value, the nature of multiplication, prime factorization and the idea that division "un-does" multiplication.

Here is the next problem that students in Grades 6 through 8 will be pondering.  I love this problem because it could not be stated more briefly or with fewer symbols.  Yet it is very sophisticated.  What is it asking?  How do I think about it?

As complicated as this problem appears, it can be solved by Middle School students.  It will require a healthy dose of common sense, creativity and persistence.

It will also require some thought about important math concepts:
What is a square root?
What does it mean to square something?
What does an equal sign mean? (Believe it or not, this is a very big idea for Middle School students to master.  It is an important step in their mathematical development.)
How do I deal with the infinite series?

Enough philosophy!  Here is the problem:

Solve This!

Solve For x: