This document discusses solving a quadratic equation for the variable n. It rewrites the equation to isolate n, then squares both sides to complete the square. Using the quadratic formula, it arrives at two possible values for n. However, one value is identified as extraneous and does not satisfy the original equation, leaving n=2 as the only valid solution.

1. Jen Markham

3. 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=

4. To solve for n, square both sides. Factorable???

5. Using the quadratic formula…

6. This then simplifies to:

7. 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, or

8. The final answer is n=2.