1. Start with the inequality:

\(x^2 - 4x + 8 < 9\)

2. Simplify the inequality:

\(x^2 - 4x + 8 - 9 < 0\)

\(x^2 - 4x - 1 < 0\)

3. Complete the square for \(x^2 - 4x\):

\((x-2)^2 - 4 - 1 < 0\)

\((x-2)^2 < 5\)

4. Solve the inequality:

\(-\sqrt{5} < x - 2 < \sqrt{5}\)

5. Add 2 to each part:

\(2 - \sqrt{5} < x < 2 + \sqrt{5}\)