Solve. Check for extraneous solutions.
-$x=\sqrt{x+13}+7$
A) $\{12\}$
B) $\{-9\}$
C) $\{3\}$
D) $\{3,12\}$

Name: Solve. Check for extraneous solutions. -$x=\sqrt{x+13}+7$ A) $\{12\}$ B) $\{-9\}$ C) $\{3\}$ D) $\{3,12\}$
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Question

Quizplus · Accepted Answer

Squaring both sides of the equation $x=\sqrt{x+13}+7$ gives $x^2 - 14x + 36 = 0$, which factors to $(x-12)(x-3)=0$. However, substituting $x=3$ back into the original equation results in an inconsistency, leaving $x=12$ as the only valid solution.

Solve Check for Extraneous Solutions x=x+13+7x=\sqrt{x+13}+7x=x+13​+7 A) {12}\{12\}{12} B) {−9}\{-9\}{−9} C) {3}\{3\}{3} D) {3,12}\{3,12\}{3,12}

Solve Check for Extraneous Solutions $x=\sqrt{x+13}+7$ A) $\{12\}$ B) $\{-9\}$ C) $\{3\}$ D) $\{3,12\}$