Question 85296
{{{x^2 - 6x -3 = 0}}}
First add 3 to both sides
{{{x^2 - 6x = 3}}}
Then take 1/2 of the coefficient of x, square it, add to both sides
{{{(6/2)^2 = 9}}}
{{{x^2 - 6x + 9 = 3 + 9}}}
{{{(x - 3)^2 = 12}}}
{{{x - 3 = 0 + 2*sqrt(3)}}}
{{{x = 3 + 2*sqrt(3)}}} answer
and
{{{(x - 3)^2 = 12}}}
{{{x - 3 = 0 - 2*sqrt(3)}}}
{{{x = 3 - 2*sqrt(3)}}} answer
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{{{2x^2 + 10x + 11 = 0}}}
divided both sides by 2
{{{x^2 + 5x  + 11/2 = 0}}}
subtract 11/2 from both sides
{{{x^2 + 5x = -(11/2)}}}
{{{x^2 + 5x + 25/4 = 25/4 - 22/4}}}
{{{(x + 5/2)^2 = 3/4}}}
{{{x + 5/2 = sqrt(3)/2}}}
{{{x = (-5 + sqrt(3))/2}}} answer
and
{{{x + 5/2 = 0 - sqrt(3)/2}}}
{{{x = (-5 - sqrt(3))/2}}} answer