Answer
$[1-\sqrt 3,1+\sqrt 3]$
Work Step by Step
Step 1. Rewrite the inequality as
$x^2-2x-2\leq0$
or
$(x-(1-\sqrt 3))(x-(1+\sqrt 3))\leq0$
and the boundary points are
$x=1\pm\sqrt 3$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(1-\sqrt 3)...(-)...(1+\sqrt 3)...(+)...$
Thus the solutions are
$1-\sqrt 3\leq x\leq 1+\sqrt 3$
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 $[1-\sqrt 3,1+\sqrt 3]$
