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$Charlotte is solving the following equation for x. (x+3)^(2)-10=2 Her first few steps are given below. {:[(x+3)^(2)=12],[x+3=+-sqrt12]:} Is it necessary for Charlotte to check her answers for extraneous solutions? Choose 1 answer: (A) Yes (B) No$

Charlotte is solving the following equation for $x$ . $\newline$ $(x+3)^{2}-10=2$ $\newline$ Her first few steps are given below. $\newline$ $\begin{aligned} (x+3)^{2} & =12 \\ x+3 & = \pm \sqrt{12} \end{aligned}$ $\newline$ Is it necessary for Charlotte to check her answers for extraneous solutions? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) $\mathrm{No}$

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Write linear functions: word problems

Full solution

Q. Charlotte is solving the following equation for

x

.

\newline

(x+3)^{2}-10=2

\newline

Her first few steps are given below.

\newline

\begin{aligned} (x+3)^{2} & =12 \\ x+3 & = \pm \sqrt{12} \end{aligned}

\newline

Is it necessary for Charlotte to check her answers for extraneous solutions?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B)

\mathrm{No}

Understand Equation and Steps: Understand the original equation and the steps Charlotte has taken. $\newline$ Charlotte is solving the equation $(x+3)^2-10=2$ . She has correctly added $10$ to both sides to isolate the squared term, resulting in $(x+3)^2 = 12$ .
Check Charlotte's Step: Check the next step Charlotte has taken. $\newline$ Charlotte has taken the square root of both sides to solve for $x$ , resulting in $x+3 = \pm\sqrt{12}$ . This is the correct method for solving a squared equation.
Determine Extraneous Solutions: Determine if checking for extraneous solutions is necessary. $\newline$ When solving equations that involve squaring or square roots, it is possible to introduce solutions that do not satisfy the original equation. This happens because squaring both sides of an equation can make a negative value positive, potentially creating solutions that weren't there before. Therefore, it is necessary to check for extraneous solutions.

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