Macey wants to determine the solutions to the quadratic equation x2−3x−2=0
.  Her first step is shown below.

x=−(−3)±(−3)2−4⋅1⋅−2√2⋅1

Compete her work to determine which of the following are the solutions to the equation.
A.3±17√2

B.−3±17√2

C.−3±17√−2

D.3±−17√2


To complete Macey's work and solve the quadratic equation \( x^2 - 3x - 2 = 0 \), let's go through each step using the quadratic formula:

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

In this case:
- \( a = 1 \)
- \( b = -3 \)
- \( c = -2 \)

Substitute these values into the formula:

\[
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-2)}}{2 \cdot 1}
\]

Simplify the terms:
1. **Calculate** \( -(-3) = 3 \).
   
   \[
   x = \frac{3 \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-2)}}{2 \cdot 1}
   \]

2. **Evaluate** \( (-3)^2 = 9 \) and \( -4 \cdot 1 \cdot (-2) = 8 \), so the expression inside the square root is:

   \[
   9 + 8 = 17
   \]

3. Substitute back:

   \[
   x = \frac{3 \pm \sqrt{17}}{2}
   \]

Thus, the solutions are:

\[
x = \frac{3 \pm \sqrt{17}}{2}
\]

### Answer
The correct answer is:
**A. \( \frac{3 \pm \sqrt{17}}{2} \)** 

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Do you want more details on any part of the solution?

### Related Questions
1. How do you derive the quadratic formula?
2. How can you determine if a quadratic equation has real or complex roots?
3. What is the importance of the discriminant \( b^2 - 4ac \) in quadratic equations?
4. How would the solutions change if \( c \) was positive?
5. What are other methods to solve a quadratic equation?

### Tip
Always check the discriminant (\( b^2 - 4ac \)) first; if it’s positive, the equation has two real solutions; if zero, one real solution; if negative, two complex solutions.

Macey wants to determine the solutions to the quadratic equation x^2 − 3x − 2 = 0. Her first step is shown below.

x = −(−3) ± (−3)^2 − 4⋅1⋅−2 / 2⋅1

Complete her work to determine which of the following are the solutions to the equation.
A. 3 ± sqrt(17) / 2
B. −3 ± sqrt(17) / 2
C. −3 ± sqrt(17) / sqrt(-2)
D. 3 ± -sqrt(17) / 2

Learn to find the solutions to the quadratic equation x^2 - 3x - 2 = 0 with step-by-step guidance using the quadratic formula. This example explores concepts in algebra and is ideal for students in Grades 9-10.

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