Which of the following describes the solution to the equation square root of c squared plus 2 c minus 4 end root is equal to square root of 1 minus 2 c end root ?

Because both sides are square roots, their radicands must be nonnegative, and the radicands must be equal. Setting them equal gives c² + 2c − 4 = 1 − 2c, or c² + 4c − 5 = 0, which factors to (c + 5)(c − 1) = 0. For c = −5, both radicands equal 11, so it is a true solution; for c = 1, the right radicand is −1, so it is not defined as a real square root. Therefore, negative 5 is true and 1 is extraneous: choice D.

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