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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Easy · Answer it here, explanation included.

Which of the following is a solution to the equation $2 x squared, minus 4, equals x squared$ ?

ExplanationShow

Choice B is correct. Subtracting x² from both sides of the given equation yields x² – 4 = 0. Adding 4 to both sides of the equation gives x² = 4. Taking the square root of both sides of the equation gives x = 2 or x = –2. Therefore, x = 2 is one solution to the original equation.

Alternative approach: Subtracting x² from both sides of the given equation yields x² – 4 = 0. Factoring this equation gives x² – 4 = (x + 2)(x – 2) = 0, such that x = 2 or x = –2. Therefore, x = 2 is one solution to the original equation.

Choices A, C, and D are incorrect and may be the result of computation errors.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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