Question 431083
Solution:We will solve this quadratic equation by completing the square:

{{{x^2-2(sqrt(2))*x/2+2/4-2/4-1=(x^2-x*sqrt(2)+(1/2))-3/2=(x-(sqrt(2))/2)^2-(3/2)}}}

Now we solve {{{(x-(sqrt(2))/2)^2=3/2}}}

{{{x-(sqrt(2))/2=+- sqrt(3/2)}}}

{{{x=sqrt(2)/2+- sqrt(3/2)}}}

{{{x[1]=(sqrt(2)+sqrt(6))/2}}} and

{{{x[2]=(sqrt(2)-sqrt(6))/2}}}

Done.