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$Pam solved a quadratic equation. Her work is shown below. In which step did Pam make an error? {:[(x+2)^(2),=16,],[x+2,=4quad" Step 1 "],[x,=2quad" Step 2 "]:} Choose 1 answer: (A) Step 1 (B) Step 2$

Pam solved a quadratic equation. Her work is shown below. $\newline$ In which step did Pam make an error? $\newline$ $(x+2)^{2}=16,$ $\newline$ $x+2=\pm 4\quad \text{Step 1}$ $\newline$ $x=-2\pm 4\quad \text{Step 2}$ $\newline$ Choose $1$ answer: $\newline$ (A) Step $1$ $\newline$ (B) Step $2$

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Math Problems

Algebra 2

Solve a quadratic equation using square roots

Full solution

Q. Pam solved a quadratic equation. Her work is shown below.

\newline

In which step did Pam make an error?

\newline

(x+2)^{2}=16,

\newline

x+2=\pm 4\quad \text{Step 1}

\newline

x=-2\pm 4\quad \text{Step 2}

\newline

Choose

1

answer:

\newline

(A) Step

1

\newline

(B) Step

2

Equation given: Pam starts with the equation $(x + 2)^2 = 16$ . $\newline$ To find the value of $x$ , she needs to take the square root of both sides of the equation. $\newline$ The square root of $(x + 2)^2$ is $x + 2$ , and the square root of $16$ is $\pm 4$ . $\newline$ This means that $x + 2$ could be either $4$ or $-4$ . $\newline$ The correct next step should be $x + 2 = 4$ or $x$ $0$ .
Taking the square root: Pam's Step $1$ shows $x + 2 = 4$ . $\newline$ This is correct for one of the possible solutions, but she has forgotten to consider the second solution $x + 2 = -4$ . $\newline$ However, since she is only showing one step at a time, this is not necessarily an error yet.
Possible values of x: Pam's Step $2$ shows x = $2$ . $\newline$ This is the correct solution for x + $2$ = $4$ . $\newline$ However, she has not shown the solution for x + $2$ = $-4$ , which would give x = $-6$ . $\newline$ The error is that she has not considered both possible solutions to the equation.