Answer
$x=1$ (multiplicity 2).
Work Step by Step
Step 1. For $x^4-2x^3+10x^2-18x+9=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm3,\pm9$
Step 2. Use synthetic division as shown in the figure to find zero(s) $x=1$ (multiplicity 2).
Step 3. Use the quotient to find other zeros: $x^2+9=0$, no real solutions.
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