Solve: \sqrt{x+6} = x. Which of the following is the only valid solution?

x = 3 Square: x+6 = x^2 \Rightarrow x^2 - x - 6 = 0 \Rightarrow (x-3)(x+2) = 0. Check: x = -2 is extraneous (since \sqrt{4} = 2 \neq -2). Valid: x = 3.

Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 3/5

\sqrt{x+6} = x

A
$x = 3$
check_circle
B
$x = 2$
C
$x = -3$
D
$x = -2$

Explanation

x+6 = x^2 \Rightarrow x^2 - x - 6 = 0 \Rightarrow (x-3)(x+2) = 0

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