Answer
$[2-\sqrt 2,2+\sqrt 2]$
Work Step by Step
Step 1. Rewrite the inequality as
$x^2-4x+2\leq0$
or
$(x-(2-\sqrt 2))(x-(2+\sqrt 2))\leq0$
and the boundary points are
$x=2\pm\sqrt 2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(2-\sqrt 2)...(-)...(2+\sqrt 2)...(+)...$,
Thus the solutions are $2-\sqrt 2\leq x\leq 2+\sqrt 2$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $[2-\sqrt 2,2+\sqrt 2]$
