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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Medium

x squared, minus x, minus 1, equals 0

What values satisfy the equation above?

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Explanation

Choice C is correct. Using the quadratic formula to solve the given expression yields x equals, the fraction with numerator negative, open parenthesis, negative 1, close parenthesis, plus or minus, the square root of open parenthesis, negative 1, close parenthesis, squared, minus, 4 times 1 times negative 1, end root, and denominator, 2 times 1, end fraction, which equals, the fraction with numerator 1, plus or minus, the square root of 5, and denominator 2. Therefore, x equals, the fraction with numerator 1 plus the square root of 5, and denominator 2 and x equals, the fraction with numerator 1 minus the square root of 5, and denominator 2 satisfy the given equation.

Choices A and B are incorrect and may result from incorrectly factoring or incorrectly applying the quadratic formula. Choice D is incorrect and may result from a sign error.