What is the solution to the equation 2x + 3 = x?

SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 9 (Medium)

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Question bank / Nonlinear equations in one variable and systems of equations in two variables

Math · Advanced MathMedium

What is the solution to the equation $\sqrt{2x + 3} = x$ ?

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Answer: 3

Square both sides: $2x + 3 = x^2$ , so $x^2 - 2x - 3 = 0$ and $(x - 3)(x + 1) = 0$ . The candidates are $x = 3$ and $x = -1$ . Check: $\sqrt{9} = 3$ works, but $\sqrt{1} = 1 \ne -1$ , so $-1$ is extraneous. The only solution is 3.

Keeping $-1$ is the common error; squaring can create solutions that don't satisfy the original equation.

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