#### Answer

$x=(3+\sqrt 6, 3-\sqrt 6)$

#### Work Step by Step

Step-1 : Subtract $3$ on both sides of the equation
$x^2-6x=-3$
Step -2 : Add the square of half of the co-efficient of $x$ to both sides.
Co-efficient of $x =-6$
Half of $-6 = \frac{1}{2}×-6=-3$
Square of $-3$ is $-3×-3=9$
The equation becomes $x^2-6x+9=-3+9$
Step-3 Factor the trinomial and simplify the right hand side.
$(x-3)^2=6$
Step-4 Use the square root property and solve for $x$
$(x-3)=±\sqrt 6 $
Step-5 Add 3 on both the sides
$x=3±\sqrt 6$
Therefore the solution set is $(3+\sqrt 6, 3-\sqrt 6)$