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$Viet solved a quadratic equation. His work is shown below. In which step did Viet make an error? 2(x-3)^(2)+4=102 {:[2(x-3)^(2)=106" Step 1 "],[(x-3)^(2)=53" Step 2 "],[x-3=+-sqrt53" Step 3 "],[x=+-sqrt53+3" Step 4 "]:} Step 3 Choose 1 answer: (A) Step 1 (B) Step 2 (C) Step 3 (D) Step 4$

Viet solved a quadratic equation. His work is shown below. $\newline$ In which step did Viet make an error? $\newline$ $2(x-3)^{2}+4=102$ $\newline$ $\begin{aligned} 2(x-3)^{2} & =106 & & \text { Step 1 } \\ (x-3)^{2} & =53 & & \text { Step 2 } \\ x-3 & = \pm \sqrt{53} & & \text { Step 3 } \\ x & = \pm \sqrt{53}+3 & & \text { Step 4 } \end{aligned}$ $\newline$ Step $3$ $\newline$ Choose $1$ answer: $\newline$ (A) Step $1$ $\newline$ (B) Step $2$ $\newline$ (C) Step $3$ $\newline$ (D) Step $4$

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Compare linear, exponential, and quadratic growth

Full solution

Q. Viet solved a quadratic equation. His work is shown below.

\newline

In which step did Viet make an error?

\newline

2(x-3)^{2}+4=102

\newline

\begin{aligned} 2(x-3)^{2} & =106 & & \text { Step 1 } \\ (x-3)^{2} & =53 & & \text { Step 2 } \\ x-3 & = \pm \sqrt{53} & & \text { Step 3 } \\ x & = \pm \sqrt{53}+3 & & \text { Step 4 } \end{aligned}

\newline

Step

3

\newline

Choose

1

answer:

\newline

(A) Step

1

\newline

(B) Step

2

\newline

(C) Step

3

\newline

(D) Step

4

Isolate the variable term: Viet starts by subtracting $4$ from both sides of the equation to isolate the term with the variable. $\newline$ $2(x-3)^2 + 4 = 102$ $\newline$ $2(x-3)^2 = 102 - 4$ $\newline$ $2(x-3)^2 = 98$
Divide both sides by $2$ : Viet then divides both sides by $2$ to solve for $(x-3)^2$ .
$2(x-3)^2 = 98$
$(x-3)^2 = \frac{98}{2}$
$(x-3)^2 = 49$
Take the square root of both sides: Viet takes the square root of both sides to solve for $x - 3$ . $x - 3 = \pm\sqrt{49}$ $x - 3 = \pm7$
Add $3$ to both sides: Viet adds $3$ to both sides to solve for $x$ . $\newline$ $x = \pm 7 + 3$ $\newline$ $x = 3 \pm 7$

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