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Real number x yields a real number

Source: 1976 AHSME Problem 2

May 14, 2014
AMC

Problem Statement

For how many real numbers xx is −(x+1)2\sqrt{-(x+1)^2} a real number?
<spanclass=′latex−bold′>(A)</span>none<spanclass=′latex−bold′>(B)</span>one<spanclass=′latex−bold′>(C)</span>two<spanclass=′latex−bold′>(D)</span>a finite number greater than two<spanclass=′latex−bold′>(E)</span>infinitely many<span class='latex-bold'>(A) </span>\text{none}\qquad<span class='latex-bold'>(B) </span>\text{one}\qquad<span class='latex-bold'>(C) </span>\text{two}\qquad<span class='latex-bold'>(D) </span>\text{a finite number greater than two}\qquad <span class='latex-bold'>(E) </span>\text{infinitely many}
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