# How do you solve x^2-6x+9<0?

We have that ${x}^{2} - 6 x + 9 = {\left(x - 3\right)}^{2} \ge 0$ hence the inequality
${x}^{2} - 6 x + 9 < 0$ has no solutions.
As you can see from the graph of ${x}^{2} - 6 x + 9$ there no values of x for which the inequality ${x}^{2} - 6 x + 9 < 0$ holds.