Soren solves the quadratic equation x2 + 8x − 9 = 0
using the quadratic formula. In which step did Soren make an error?

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Clear Check

Soren did not make an error.

Step 1: Soren should subtract 36 underneath the radical instead of add.

Step 2: Soren must divide -8 by 2 before simplifying the radical.

Step 3: Soren did not divide by 2 for each of the resulting numerators.

To identify the error Soren might have made while solving the quadratic equation using the quadratic formula, let’s break down the correct process.

Given quadratic equation: 

\[ x^2 + 8x - 9 = 0 \]

The quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = 1 \), \( b = 8 \), and \( c = -9 \).

### Step-by-Step Solution

1. **Calculate the discriminant**:  
   \[
   b^2 - 4ac = 8^2 - 4(1)(-9) = 64 + 36 = 100
   \]

2. **Apply the quadratic formula**:
   \[
   x = \frac{-8 \pm \sqrt{100}}{2(1)} = \frac{-8 \pm 10}{2}
   \]

3. **Find the solutions**:
   \[
   x_1 = \frac{-8 + 10}{2} = \frac{2}{2} = 1
   \]
   \[
   x_2 = \frac{-8 - 10}{2} = \frac{-18}{2} = -9
   \]

So, the correct roots are \( x = 1 \) and \( x = -9 \).

### Analyzing the Steps Provided:

1. **Step 1: "Soren should subtract 36 underneath the radical instead of add."**  
   This statement is incorrect because the correct discriminant calculation involves adding 36, as shown in the correct step-by-step process.

2. **Step 2: "Soren must divide -8 by 2 before simplifying the radical."**  
   This is incorrect because in the quadratic formula, the division by 2 happens only after calculating the expression under the square root and combining it with \(-b\).

3. **Step 3: "Soren did not divide by 2 for each of the resulting numerators."**  
   This is incorrect since Soren should divide the final results by 2 after determining the expression from the quadratic formula.

### Conclusion:

Soren did not make an error in solving the quadratic equation using the quadratic formula. Thus, the correct choice is:

**"Soren did not make an error."**

Would you like to dive into any details or have further questions? Here are some related queries:

1. How do we calculate the discriminant for any quadratic equation?
2. What happens if the discriminant is negative?
3. Can the quadratic formula be used for non-quadratic equations?
4. What are alternative methods to solve quadratic equations?
5. How does the quadratic formula change if the coefficient \(a\) is not 1?

**Tip:** Always ensure to simplify each step fully before moving on to the next to avoid calculation errors.

Explore how to identify errors in solving quadratic equations using the quadratic formula. This detailed analysis covers the discriminant, correct application of the quadratic formula, and step-by-step error analysis. Suitable for high school students and anyone interested in quadratic equations.

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