I can't quite get the meaning of this expression. "Was" is confusing me. Is it just a mistype of "with"?
"The experiment to be carried out was a success."
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The sentence is "The experiment was a success." Or: "The experiment succeeded."
The part of it which seems to be confusing you is "to be carried out." This phrase means which was done. It is superfluous. It is unnecessary. Of course the experiment was done; there is no need to say so. As it happens, emphasizing that it was carried out has accomplished only one thing: confusing you.
The phrase " Carry out" means to continue to an end point.
The sentence probably means that
The experiment was decided to be continued until it got a conclusion, and it turned out to be a successful one
A potential source of confusion here is that the ellipsis is unpredictable before one sees the second part of the sentence.
The experiment to be carried out was a success.
The experiment which was to be carried out was a success (proved to have a successful outcome).
The experiment to be carried out will hopefully be a success.
The experiment which is (going) to be carried out will hopefully be a success.
(See at http://oxforddictionaries.com/words/hopefully for the licensing of the pragmatic-marker usage of 'hopefully'.)