The solution is $x=1$.
Work Step by Step
$\sqrt 2-x=x$ Square both sides: $2-x=x^2$ $x^2+x-2=0$ $x-1=0$ or $x+2=0$ $x=1$ or $x=-2$ Check: $\sqrt 2-1=x$ $1=\sqrt 1$ $\sqrt 2-(-2)=-2$ $2=-2$ The solution is $x=1$.
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