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Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 4/5

Solve: x+4=x−2\sqrt{x+4} = x - 2.

  • A

    x=0x = 0

  • B

    x=−1x = -1

  • C

    x=5x = 5

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  • D

    x=0x = 0 and x=5x = 5

Explanation

Square: x+4=x2−4x+4⇒x2−5x=0⇒x=0x + 4 = x^2 - 4x + 4 \Rightarrow x^2 - 5x = 0 \Rightarrow x = 0 or x=5x = 5. Check x=0x = 0: 4=2≠−2\sqrt{4} = 2 \neq -2, extraneous. Valid x=5x = 5.

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