Solve the Quadratic Inequality: x²-6x+9 < 0

To solve the inequality $x^2 - 6x + 9 < 0$, we first factor the quadratic expression as $(x-3)^2$.

Note that $(x-3)^2 \geq 0$ for all real numbers $x$ because it is a square. Furthermore, $(x-3)^2$ equals zero only when $x = 3$.

This means that the expression $(x-3)^2$ never actually becomes negative for any real $x$. The vertex of the parabola, a perfect square, simply touches the x-axis at $x = 3$ but does not dip below.

Therefore, there is no solution to the inequality $x^2 - 6x + 9 < 0$ over the real numbers.

The conclusion is that there is no negative domain.