Anna solved the equation (x+4)2=2 using the following steps.

Review her work carefully, and then follow the instructions.

Line 1: (x+4)2=2
Line 2: x+4=±2
Line 3: x+4−4=−4±2
Line 4: x=−4±2

Which statement identifies a mistake Anna made, if any?

Responses

In Line 2, she should have squared both sides of the equation.

In Line 2, she should have squared both sides of the equation.

She did not make a mistake. Her answer is correct.

She did not make a mistake. Her answer is correct.

In Line 3, she should have added 4 to both sides of the equation instead of subtracting 4.

In Line 3, she should have added 4 to both sides of the equation instead of subtracting

In Line 4, she should have found only one solution, which is

Let's analyze Anna's solution step by step.

### Step 1: 
\[
(x + 4)^2 = 2
\]
This is the original equation, and it's correct.

### Step 2: 
\[
x + 4 = \pm 2
\]
This step is incorrect. Anna mistakenly assumed that squaring both sides would allow her to take the square root directly and get \( x + 4 = \pm 2 \). However, when solving a quadratic equation, the correct approach should involve expanding and then rearranging terms.

### Correct Approach:
1. Start with:
   \[
   (x + 4)^2 = 2
   \]
2. Take the square root of both sides:
   \[
   x + 4 = \pm \sqrt{2}
   \]
   Notice that the square root of 2 is used instead of just 2.

The correct mistake statement is:  
**In Line 2, she should have taken the square root of both sides instead of assuming square directly.**

Would you like me to elaborate on the correct solution further, or do you have more questions? 

### Here are 5 relative questions:
1. What are the next steps after taking the square root of both sides?
2. How can you factor quadratic equations?
3. What is the discriminant of a quadratic equation and why is it useful?
4. How do you handle equations involving complex numbers?
5. What are other methods to solve quadratic equations besides factoring and completing squares?

**Tip:** Always remember to carefully consider when to apply the square root and note the implications of \(\pm\).

Explore how to solve the quadratic equation (x+4)^2 = 2 step-by-step. Analyze common mistakes and learn the correct approach. Suitable for high school students studying quadratic equations.

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