Question 100447
Solve by completing the square
{{{x^2-6x-3=0}}}
First move the term without a variable to the other side of the equal sign
In this problem we'll move the 3
{{{x^2-6x=3}}}
Next divide all terms by the number with {{{x^2}}}
In this problem there is a 1 so essential we can skip this step.
But I will show the work just to be clear.
{{{x^2-6x=3}}}
{{{(x^2)/1-(6x)/1=3/1}}}
{{{x^2-6x=3}}}
Now take half of the number with x and square it
The number with x in this problem is -6
Half of -6 is -3
-3 squared is 9
Now add 9 to both sides of the equal sign
{{{x^2-6x+9=3+9}}}
{{{x^2-6x+9=12}}}
Next factor the left hand side to convert it to its squared form
The left side of the equation is {{{x^2-6x+9}}}
this is converts to {{{(x-3)^2}}} because 
{{{(x-3)(x-3)=x^2-6x+9}}}
So now our problem looks like this:
{{{(x-3)^2=12}}}
Next take the square root of both sides remember that the right side will be
plus or minus the square root
{{{sqrt((x-3)^2)=(plus_minus)sqrt(12)}}}
{{{x-3=(plus_minus)sqrt(12)}}}
Finally solve for x
{{{x=3-sqrt(12)}}}
and
{{{x=3+sqrt(12)}}}
These are the TWO answers for x