Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { x ^ { 2 } + 6 x + 16 } = 4$
A) $\{ - 6 \}$
B) $\{ - 6,6 \}$
C) $\{ 0 , - 6 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

First, square both sides of the equation to eliminate the radical:
\begin{align*}
\sqrt{x^2+6x+16}&=4\
\Rightarrow \quad (\sqrt{x^2+6x+16})^2&=4^2\
\Rightarrow \quad x^2+6x+16&=16\
\Rightarrow \quad x^2+6x&=0\
\Rightarrow \quad x(x+6)&=0\
\Rightarrow \quad x&=0 	ext{ or } x=-6\
\end{align*}
As a result, the solutions to the equation are $x=0$ and $x=-6$. However, we must make sure that both $x=0$ and $x=-6$ satisfy the original equation. If we plug them in, we see that $x=0$ does not work, but $x=-6$ does:
\begin{align*}
\sqrt{(-6)^2+6(-6)+16} &= \sqrt{36-36+16}\
&=\sqrt{0} \
&=0\
&
eq 4
\end{align*}

So, the only solution that works is $x=-6$, which is choice C.

Write the Word or Phrase That Best Completes Each Statement x2+6x+16=4\sqrt { x ^ { 2 } + 6 x + 16 } = 4x2+6x+16​=4

Write the Word or Phrase That Best Completes Each Statement $\sqrt { x ^ { 2 } + 6 x + 16 } = 4$