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