Solve: \sqrt{2x+1} = x - 1.

x = 4 only Square: 2x + 1 = x^2 - 2x + 1 \Rightarrow x^2 - 4x = 0 \Rightarrow x = 0 or x = 4. Check x = 0: \sqrt{1} = 1 \neq -1, extraneous. Check x = 4: \sqrt{9} = 3 = 4 - 1, valid.

Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

\sqrt{2x+1} = x - 1

A
$No real solution$
B
$x = 0$
C
$x = 0$
D
$x = 4$
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Explanation

2x + 1 = x^2 - 2x + 1 \Rightarrow x^2 - 4x = 0 \Rightarrow x = 0

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